Yuri Tschinkel's Publications

Publications



Books edited

[1] Rational points on algebraic varieties, (with E. Peyre), Progress in Mathematics 199, Birkhäuser, (2001)

[2] Arithmetic of higher-dimensional algebraic varieties, (with B. Poonen), Progress in Mathematics 226, Birkhäuser, (2003)

[3] Mathematisches Institut, Seminars 2003/04, Universitätsverlag Göttingen, (2004)

[4] Geometric methods in algebra and number theory, (with F. Bogomolov), Progress in Mathematics 235, Birkhäuser, (2004)

[5] Mathematisches Institut, Seminars 2004, Universitätsverlag Göttingen, (2004)

[6] Mathematisches Institut, Seminars 2004/05, Universitätsverlag Göttingen, (2005)

[7] Mathematisches Institut, Summer school Algebraic groups, Göttingen 2005, Universitätsverlag Göttingen (2007)

[8] Analytic Number Theory / A tribute to Gauss and Dirichlet, (with W. Duke), CMI Proceedings series, AMS (2007)

[9] Eisenstein series and applications, (with W.T. Gan and S. Kudla), Progress in Mathematics 258, Birkhäuser, (2008)

[10] Algebra, Arithmetic and Geometry - Manin Festschrift, (with Yu. Zarhin), Progress in Mathematics 269 and 270, Birkhäuser, (2007)

[11] Arithmetic geometry, Proceedings of the Clay Summer School Göttingen 2006, (with H. Darmon and B. Hassett), CMI Proceedings series, AMS, (2009)

[12] Higher-dimensional geometry over finite fields, Advanced Study Institute 2007 Proceedings, (with D. Kaledin), IOS Press, (2008)

[13] Mathematisches Institut, Trends in mathematics, Courant Colloquium Göttingen, (with R. Meyer and Th. Schick), Universitätsverlag Göttingen, (2008)

[14] Cohomological and geometric approaches to rationality problems, (with F. Bogomolov), Progress in Mathematics 282, Birkhäuser, (2009)

[15] Birational geometry, rational curves, and arithmetic, (with F. Bogomolov and B. Hassett), Springer Verlag, (2013)

[16] Rational points, rational curves and entire holomorphic curves on projective varieties, (with C. Gasbarri, S.S.-Y. Lu and M. Roth), in preparation


Research papers

[1] Rational points of bounded height on Fano varieties (with J. Franke, Yu. I. Manin), Inventiones Math., 95, 421-435, (1989)

[2] Points of bounded height on Del Pezzo surfaces, (with Yu. I. Manin), Compositio Math., 85(3), 315-332, (1993)

[3] Rational points of bounded height on compactifications of anisotropic tori, (with V. Batyrev), Intern. Math. Research Notices, 12, 591-635, (1995)

[4] Height zeta functions of toric varieties, (with V. Batyrev), Algebraic geometry, 5, (Manin's Festschrift), Journ. Math. Sci., 82, no. 1, 3220-3239, (1996)

[5] Rational points on some Fano cubic bundles, (with V. Batyrev), C. R. Acad. Sci., Paris, 323, Ser. I, 41-46, (1996)

[6] Height zeta functions of twisted products, (with M. Strauch), Math. Res. Letters, 4, 273-282, (1997)

[7] Manin's conjecture for toric varieties, (with V. Batyrev), Journ. of Alg. Geom., 7, no. 1, 15-53, (1998)

[8] Tamagawa numbers of polarized algebraic varieties, (with V. Batyrev), Asterisque, 251, 299-340, (1998)

[9] Height zeta functions of toric bundles over flag varieties, (with M. Strauch), Selecta Math. (N.S.), 5, no. 3, 325-396, (1999)

[10] Tamagawa numbers of diagonal cubic surfaces, (with E. Peyre), Math. Comp., 70, 367-387, (2001)

[11] Torseurs arithmetiques et espaces fibres, (with A. Chambert-Loir), "Rational points on algebraic varieties", 37-70, Progress in Math. 199, Birkhäuser, (2001)

[12] Rational points on quartics, (with J. Harris), Duke Math. Journ., 104, no. 3, 477-500, (2000)

[13] On the density of rational points on elliptic fibrations, (with F. Bogomolov), Journ. Reine und Angew. Math., 511, 87-93, (1999)

[14] Density of rational points on Enriques surfaces, (with F. Bogomolov), Math. Res. Letters, 5, 623-628, (1998)

[15] Fonctions zeta des hauteurs des espaces fibres, (with A. Chambert-Loir), "Rational points on algebraic varieties", 71-115, Progress in Math. 199, Birkhäuser, (2001)

[16] Density of rational points on elliptic K3 surfaces, (with F. Bogomolov), Asian Journ. of Math., 4, no. 2, 351-368, (2000)

[17] Points of bounded height on equivariant compactifications of vector groups I, (with A. Chambert-Loir), Compositio Math., 124(1), 65-93, (2000)

[18] Tamagawa numbers of diagonal cubic surfaces of higher rank, (with E. Peyre), "Rational points on algebraic varieties", 275-305, Progress in Math. 199, Birkhäuser, (2001)

[19] Geometry of equivariant compactifications of Gan, (with B. Hassett), Intern. Math. Research Notices, 22, 1211-1230, (1999)

[20] Points of bounded height on equivariant compactifications of vector groups II, (with A. Chambert-Loir), Journ. of Number Theory, 85, no. 2, 172-188, (2000)

[21] Rational curves on holomorphic symplectic fourfolds, (with B. Hassett), GAFA, 11, no. 6, 1201-1228, (2001), Erratum

[22] Abelian fibrations and rational points on symmetric products, (with B. Hassett), Intern. Journ. of Math., 11, no. 9, 1163-1176, (2000)

[23] On the distribution of points of bounded height on equivariant compactifications of vector groups, (with A. Chambert-Loir), Inventiones Math., 148, no. 2, 421-452, (2002)

[24] Monodromy of elliptic surfaces, (with F. Bogomolov), "Galois Groups and Fundamental Groups", (L. Schneps, ed.), 167-181, MSRI Publications vol. 41, Cambridge Univ. Press, (2003)

[25] Density of integral points on algebraic varieties, (with B. Hassett), "Rational points on algebraic varieties", 169-197, Progress in Math. 199, Birkhäuser, (2001)

[26] Lagrangian subvarieties of abelian fourfolds, (with F. Bogomolov), Asian Journ. of Math., 4, no. 1, 19-36, (2000)

[27] Commuting elements in Galois groups of function fields, (with F. Bogomolov), "Motives, Polylogarithms and Hodge theory", (F. Bogomolov, L. Katzarkov eds.), 75-120, International Press, (2002)

[28] Distribution of rational points on equivariant compactifications of inner forms of reductive groups, (with J. Shalika and R. Takloo-Bighash), 50 pp., (2001)

[29] Rationality of moduli of elliptic fibrations with fixed monodromy, (with F. Bogomolov and T. Petrov), GAFA, 12, no. 6, 1105-1160, (2002)

[30] Simple examples of symplectic four-manifolds with exotic properties, (with F. Bogomolov), Acta Appl. Math., 75, no. 1-3, 25-28, (2003)

[31] On the effective cone of the moduli space of pointed rational curves, (with B. Hassett), "Topology and Geometry" (A. J. Berrick, M. C. Leung, X. W. Xu eds.), Contemporary Math., 314, 83-96, (2002)

[32] Rational points and automorphic forms, (with J. Shalika and R. Takloo-Bighash), "Contributions to Automorphic Forms, Geometry, and Number Theory", (H. Hida, D. Ramakrishnan, F. Shahidi eds.), 733-742, Johns Hopkins University Press, (2004)

[33] Height zeta functions of equivariant compactifications of the Heisenberg group, (with J. Shalika), "Contributions to Automorphic Forms, Geometry, and Number Theory", (H. Hida, D. Ramakrishnan, F. Shahidi eds.), 743-771, Johns Hopkins University Press, (2004)

[34] Unramified correspondences, (with F. Bogomolov), "Algebraic Number Theory and Algebraic Geometry" (S. Vostokov, Yu. Zarhin eds.), Contemporary Math. 300, 17-26, (2002)

[35] Integral points on punctured abelian surfaces, (with A. Kresch), "Algorithmic number theory", Proceedings of ANTS V, 198-204, LNCS 2369, Springer, (2002)

[36] Integral points and effective cones of moduli spaces of stable maps, (with B. Hassett), Duke Math. Journ., 120, no. 3, 577-599, (2003)

[37] Special elliptic fibrations, (with F. Bogomolov), Proceedings of the Fano Conference, (A. Collino, A. Conte, M. Marchisio, eds.), 223-234, (2004)

[38] On the arithmetic of Del Pezzo surfaces of degree two, (with A. Kresch), Proceedings London Math. Soc., (3) 89, 545-569, (2004)

[39] Reconstruction of function fields, (with F. Bogomolov), GAFA, 18, no. 2, 400-462, (2008)

[40] Universal torsors and Cox rings, (with B. Hassett), "Arithmetic of higher-dimensional algebraic varieties", 149-173, Progress in Math. 226, Birkhäuser, (2003)

[41] Rational points on compactifications of semi-simple groups of rank 1, (with J. Shalika and R. Takloo-Bighash), "Arithmetic of higher-dimensional algebraic varieties", 205-233, Progress in Math. 226, Birkhäuser, (2003)

[42] Rational curves and points on K3 surfaces, (with F. Bogomolov), Amer. Journ. of Math., 127, no. 4, 825-835, (2005)

[43] Couniformization of curves over number fields, (with F. Bogomolov), "Geometric methods in algebra and number theory", 43-57, Progress in Math. 235, Birkhäuser, (2004)

[44] Weak approximation over function fields, (with B. Hassett), Inventiones Math., 163, no. 1, 171-190, (2006)

[45] Curves in abelian varieties over finite fields, (with F. Bogomolov), Intern. Math. Research Notices, 4, 233-238, (2005)

[46] Approximation at places of bad reduction for rationally connected varieties, (with B. Hassett), Pure and Applied Math Quarterly, Bogomolov Festschrift, 4, no. 3, 743-766, (2008)

[47] Potential density of rational points for K3 surfaces over function fields, (with B. Hassett), Amer. Journ. of Math., 130, no. 5, 1263-1278, (2008)

[48] Algebraic varieties over small fields, (with F. Bogomolov), Special semester on Arithmetic geometry at Centro Ennio De Giorgi, 53-71, (2007)

[49] Universal torsors over Del Pezzo surfaces and rational points, (with U. Derenthal), "Equidistribution in Number theory, An Introduction", (A. Granville, Z. Rudnick eds.), 169-196, NATO Science Series II, 237, Springer, (2007)

[50] Rational points on compactifications of semi-simple groups, (with J. Shalika and R. Takloo-Bighash), Journ. of the AMS, 20, 1135-1186, (2007)

[51] Weak approximation for hypersurfaces of low degree, (with B. Hassett), Proceedings Symp. Pure Math. AMS, 80 (2), 937-955, (2009)

[52] Effectivity of Brauer-Manin obstructions, (with A. Kresch), Advances in Math., 218, no. 1, 1-27, (2008)

[53] Log Fano varieties over function fields of curves, (with B. Hassett), Inventiones Math., 171, no. 1., 7-21, (2008)

[54] Brauer-Manin obstructions for integral points, (with A. Kresch), Bulletin LMS, 40, no. 6, 995-1001, (2008)

[55] Moving and ample cones of holomorphic symplectic fourfolds, (with B. Hassett), GAFA, 19, no. 4, 1065-1080, (2009)

[56] A Torelli theorem for curves over finite fields, (with F. Bogomolov and M. Korotiaev), Pure and Applied Math Quarterly, Tate Festschrift, 6, no. 1, 245-294, (2010)

[57] Flops on holomorphic symplectic fourfolds and determinantal cubic hypersurfaces, (with B. Hassett), Journ. Inst. Math. Jussieu, 6, no. 1, 125-153, (2010)

[58] On a theorem of Tate, (with F. Bogomolov), CEJM, 6, no. 3, 343-350, (2008)

[59] Unramified cohomology of finite groups of Lie type, (with F. Bogomolov and T. Petrov), "Rationality problems", 55-73, Progress in Math. 282, Birkhäuser, (2009)

[60] Milnor K2 and field homomorphisms, (with F. Bogomolov), Surveys in Differential Geometry XIII, 223-244, (2009)

[61] Co-fibered products of algebraic curves, (with F. Bogomolov), CEJM, 7, no. 3, 382-386, (2009)

[62] Igusa integrals and volume asymptotics in analytic and adelic geometry, (with A. Chambert-Loir), Confluentes Mathematici, 2, no. 3, 351-429, (2010)

[63] Constructing rational curves on K3 surfaces, (with F. Bogomolov and B. Hassett), Duke Math. Journ., 157, no. 3, 535-550, (2011)

[64] Intersection numbers of extremal rays on holomorphic symplectic varieties, (with B. Hassett), Asian Journ. of Math., 14, no. 3., 303-322, (2010)

[65] Effectivity of Brauer-Manin obstructions on surfaces, (with A. Kresch), Advances in Math., 226, 4131-4144, (2011)

[66] Monodromy and rational curves on holomorphic symplectic varieties, (with B. Hassett), 9 pp., (2009)

[67] Integral points of bounded height on partial equivariant compactifications of vector groups, (with A. Chambert-Loir), Duke Math. Journal, 161, no. 15, 2799-2836, (2012)

[68] Reconstruction of higher-dimensional function fields, (with F. Bogomolov), Moscow Math. Journal, 11, no. 2, 185-204, (2011)

[69] Hodge theory and Lagrangian planes on generalized Kummer fourfolds, (with B. Hassett), Moscow Math. Journal, 13, no. 1, 33-56, (2013)

[70] Integral points of bounded height on toric varieties, (with A. Chambert-Loir), 28 pp., (2010)

[71] Introduction to birational anabelian geometry, (with F. Bogomolov), in "Current Developments in Algebraic Geometry", (L. Caporaso, J. McKernan, M. Mustata, M. Popa eds.), 17-63, MSRI Publications vol. 59, Cambridge Univ. Press, (2012)

[72] Characterizing projective spaces on deformations of Hilbert schemes of K3 surfaces, (with D. Harvey and B. Hassett), Comm. Pure and Applied Math., 65, no. 2., 264-286, (2012)

[73] Height zeta functions of equivariant compactifications of semi-direct products of algebraic groups, (with S. Tanimoto), Contemporary Math., 566, 119-157, (2012)

[74] Integral points of bounded height on compactifications of semi-simple groups, (with R. Takloo-Bighash), Amer. Journ. of Math., 135, no. 5, 1433-1448, (2013)

[75] Spaces of sections of quadric surface fibrations over curves, (with B. Hassett), Contemporary Math., 564, 227-249, (2012)

[76] Multiple mixing for adele groups and rational points, (with A. Gorodnik, R. Takloo-Bighash), 22 pp., (2011)

[77] Galois theory and projective geometry, (with F. Bogomolov), Comm. Pure and Applied Math. 66, no. 9, 1335-1359, (2013)

[78] Effective computation of Picard groups and Brauer-Manin obstructions of degree two K3 surfaces over number fields, (with B. Hassett and A. Kresch), Rendiconti del Circolo Matematico di Palermo, 62, 137-151, (2013)

[79] Embedding pointed curves in K3 surfaces, (with B. Hassett), 28 pp., (2012), to appear in Math. Zeitschrift

[80] Quartic Del Pezzo surfaces over function fields of curves, (with B. Hassett), CEJM, 12(3), 395-420, (2014)

[81] Balanced line bundles and equivariant compactifications of homogeneous spaces, (with B. Hassett and S. Tanimoto), Intern. Math. Research Notices, (2014)

[82] Mori cones of holomorphic symplectic varieties of K3 type, (with A. Bayer and B. Hassett), 10 pp., to appear in Ann. Sci. ENS

[83] On the moduli space of degree 4 Del Pezzo surfaces, (with B. Hassett and A. Kresch), 37 pp., (2013)

[84] Universal spaces for unramified Galois cohomology, (with F. Bogomolov), 34 pp., (2014)

[85] Height zeta functions of equivariant compactifications of unipotent groups, (with J. Shalika), 45 pp., (2014)

[86] Variation of Neron-Severi ranks of reductions of K3 surfaces, (with E. Costa), 12 pp., to appear in Experimental Math.

[87] Rational points on K3 surfaces and derived equivalence, (with B. Hassett), 23 pp., (2014)

[88] Balanced line bundles on Fano varieties, (with B. Lehmann and S. Tanimoto), 49 pp., (2014)



Surveys and technical reports

[1] Rational points and heights, (Russian), Proceedings of the XXVIth All-Union Sci. Stud. Conference (Novosibirsk, 1988), Novosibirsk. Gos. Univ., 80-84, (1988)

[2] Generalised Chatelet varieties, (Russian), Proceedings of the conference "Constructive Methods and Algorithms in Number Theory", Academy of Sci. BSSR, Minsk, USSR, 163, (1989)

[3] Arithmetic of algebraic surfaces, Ph.D. Thesis, M.I.T., (1992)

[4] Finite heights and rational points on surfaces, Advances in number theory (Kingston, ON, 1991), 319--329, Oxford Sci. Publ., Oxford Univ. Press, New York, (1993)

[5] On rational points, Proceedings "Intern. Conf. Algebraic Geometry", Sendai, 157-172, (1993)

[6] Rational points on toric varieties, (with V. Batyrev), Number theory (Halifax, NS, 1994), CMS Conf. Proc., 15, AMS, Providence, RI, 39-48, (1995)

[7] Height zeta functions, Proceedings Arbeitstagung Bonn, (1997)

[8] Lectures on height zeta functions of toric varieties, "Geometry of Toric Varieties", Seminaires et Congres, 6, 227-247, (2002)

[9] Resolution of singularities, (with F. Bogomolov), Review of a book by H. Hauser et al., Bulletin AMS, 39, 95-100, (2002)

[10] Fujita's program and rational points, "Higher Dimensional Varieties and Rational Points", (K. J. Böröczky, J. Kollár, T. Szamuely eds.), Bolyai Society Mathematical Studies 12, 283-310, Springer Verl., (2003)

[11] On curve correspondences, (with F. Bogomolov), "Communications in Arithmetic Fundamental Groups and Galois Theory", RIMS, 157-166, (2002)

[12] About the cover: On the distribution of primes - Gauss' tables, Bulletin AMS, 43, 89-91, (2006)

[13] Geometry over nonclosed fields, ICM talk, 15 pp., (2006)

[14] About the cover: Invariants, Bulletin AMS, 44, 433-437, (2007)
Minkowski to Hilbert, February 2, 1892, 1, 2, 3, 4 (courtesy of Staats- und Universitätsbibliothek Göttingen)

[15] The Felix Klein protocols, (with E. Chislenko), Notices AMS, 54 (8), 958-968, (2007)

[16] Algebraic varieties with many rational points, Clay Summer School Proceedings, 92 pp., (2008)

[17] Die Felix Klein Protokolle, 11 pp., (2008)