Yuri Tschinkel

2019

A very general quartic double fourfold is not stably rational

Hassett, B., Pirutka, A. & Tschinkel, Y., Jan 1 2019, In : Algebraic Geometry. 6, 1, p. 64-75 12 p.

Research output: Contribution to journal › Article

Threefolds

Quartic

Cover

Homomorphisms of multiplicative groups of fields preserving algebraic dependence

Bogomolov, F., Rovinsky, M. & Tschinkel, Y., Sep 15 2019, In : European Journal of Mathematics. 5, 3, p. 656-685 30 p.

Research output: Contribution to journal › Article

Homomorphisms

Multiplicative

Valuation

Models of brauer–severi surface bundles

Kresch, A. & Tschinkel, Y., Jul 1 2019, In : Moscow Mathematical Journal. 19, 3, p. 549-595 47 p.

Research output: Contribution to journal › Article

Projective Variety

Rationality

Bundle

Roots

Model

Models of Triple Covers

Kresch, A. & Tschinkel, Y., May 1 2019, In : Mathematical Notes. 105, 5-6, p. 795-797 3 p.

Research output: Contribution to journal › Article

Algebraic Variety

Cover

Model

On stable rationality of Fano threefolds and del Pezzo fibrations

Hassett, B. & Tschinkel, Y., Jun 1 2019, In : Journal fur die Reine und Angewandte Mathematik. 2019, 751, p. 275-287 13 p.

Research output: Contribution to journal › Article

del operator

Fibration

Threefolds

Rationality

Specialization of birational types

Kontsevich, M. & Tschinkel, Y., Jan 1 2019, In : Inventiones Mathematicae.

Research output: Contribution to journal › Article

Specialization

2018

Balanced line bundles on Fano varieties

Lehmann, B., Tanimoto, S. & Tschinkel, Y., Oct 1 2018, In : Journal fur die Reine und Angewandte Mathematik. 2018, 743, p. 91-131 41 p.

Research output: Contribution to journal › Article

Fano Variety

Geometric Invariants

Minimal Model

Line Bundle

Threefolds

Stable rationality of Brauer–Severi surface bundles

Kresch, A. & Tschinkel, Y., Jan 1 2018, (Accepted/In press) In : Manuscripta Mathematica.

Research output: Contribution to journal › Article

Rational Surface

Rationality

Bundle

Linear Systems

Stable rationality of quadric surface bundles over surfaces

Hassett, B., Pirutka, A. & Tschinkel, Y., Jan 1 2018, In : Acta Mathematica. 220, 2, p. 341-365 25 p.

Research output: Contribution to journal › Article

Quadric

Rationality

Bundle

Torsion of elliptic curves and unlikely intersections

Bogomolov, F., Fu, H. & Tschinkel, Y., Jan 1 2018, Geometry and Physics: A Festschrift in Honour of Nigel Hitchin. Oxford University Press, Vol. 1. p. 19-38 20 p.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Torsion Points

Elliptic Curves

Torsion

Intersection

Line

2017

Rational points on K3 surfaces and derived equivalence

Hassett, B. & Tschinkel, Y., 2017, Progress in Mathematics. Springer Basel, Vol. 320. p. 87-113 27 p. (Progress in Mathematics; vol. 320).

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Derived Equivalence

K3 Surfaces

Rational Points

Universal spaces for unramified galois cohomology

Bogomolov, F. & Tschinkel, Y., 2017, Progress in Mathematics. Springer Basel, Vol. 320. p. 57-86 30 p. (Progress in Mathematics; vol. 320).

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Galois Cohomology

Universal Space

Algebraic Variety

Galois field

Closure

2016

Extremal rays and automorphisms of holomorphic symplectic varieties

Hassett, B. & Tschinkel, Y., 2016, In : Progress in Mathematics. 315, p. 73-95 23 p.

Research output: Contribution to journal › Comment/debate

Half line

Automorphisms

Height Zeta Functions of Equivariant Compactifications of Unipotent Groups

Shalika, J. & Tschinkel, Y., Apr 1 2016, In : Communications on Pure and Applied Mathematics. 69, 4, p. 693-733 41 p.

Research output: Contribution to journal › Article

Compactification

Riemann zeta function

Equivariant

2015

Balanced Line Bundles and Equivariant Compactifications of Homogeneous Spaces

Hassett, B., Tanimoto, S. & Tschinkel, Y., 2015, In : International Mathematics Research Notices. 2015, 15, p. 6375-6410 36 p.

Research output: Contribution to journal › Article

Geometric Invariants

Line Bundle

Homogeneous Space

Compactification

Equivariant

Mori cones of holomorphic symplectic varieties of K3 type

Bayer, A., Hassett, B. & Tschinkel, Y., Aug 1 2015, In : Annales Scientifiques de l'Ecole Normale Superieure. 48, 4, p. 941-950 10 p.

Research output: Contribution to journal › Article

Hilbert Scheme

K3 Surfaces

Cone

Multiple mixing for adele groups and rational points

Gorodnik, A., Takloo-Bighash, R. & Tschinkel, Y., Sep 1 2015, In : European Journal of Mathematics. 1, 3, p. 441-461 21 p.

Research output: Contribution to journal › Article

Rational Points

Algebraic Groups

Simple group

Compactification

Asymptotic Formula

Stable rationality and conic bundles

Hassett, B., Kresch, A. & Tschinkel, Y., Sep 16 2015, (Accepted/In press) In : Mathematische Annalen.

Research output: Contribution to journal › Article

Rational Surface

Rationality

Bundle

2014

Embedding pointed curves in K3 surfaces

Hassett, B. & Tschinkel, Y., Nov 12 2014, In : Mathematische Zeitschrift. 278, 3-4, p. 927-953 27 p.

Research output: Contribution to journal › Article

K3 Surfaces

Rational Curves

Cross ratio

Curve

del operator

Geometrie der zahlen - zum 150. geburtstag von Hermann Minkowski

Tschinkel, Y., 2014, In : Mitteilungen der DMV. 22, 4, p. 228-233

Research output: Contribution to journal › Article

Quartic del Pezzo surfaces over function fields of curves

Hassett, B. & Tschinkel, Y., 2014, In : Central European Journal of Mathematics. 12, 3, p. 395-420 26 p.

Research output: Contribution to journal › Article

Del Pezzo Surfaces

Fibration

Function Fields

Quartic

Curve

Rational points on K3 surfaces and derived equivalence

Tschinkel, Y. & Hassett, B., 2014, 30 p.

Research output: Other contribution

Universal spaces for unramified Galois cohomology

Tschinkel, Y. & Bogomolov, F., 2014, 31 p.

Research output: Other contribution

Variation of Néron-Severi ranks of reductions of K3 surfaces

Costa, E. & Tschinkel, Y., Oct 2 2014, In : Experimental Mathematics. 23, 4, p. 475-481 7 p.

Research output: Contribution to journal › Article

K3 Surfaces

Modulo

Quartic

Statistics

2013

Birational geometry, rational curves, and arithmetic

Bogomolov, F., Hassett, B. & Tschinkel, Y., Jan 1 2013, Springer New York. 319 p.

Research output: Book/Report › Book

Rational Curves

Algebraic Variety

Integral Points

Rational Solutions

Integral Solution

Effective computation of Picard groups and Brauer-Manin obstructions of degree two K 3 surfaces over number fields

Hassett, B., Kresch, A. & Tschinkel, Y., Apr 2013, In : Rendiconti del Circolo Matematico di Palermo. 62, 1, p. 137-151 15 p.

Research output: Contribution to journal › Article

Brauer Group

Picard Group

K3 Surfaces

Obstruction

Number field

Galois theory and projective geometry

Bogomolov, F. & Tschinkel, Y., Sep 2013, In : Communications on Pure and Applied Mathematics. 66, 9, p. 1335-1359 25 p.

Research output: Contribution to journal › Article

Galois Theory

Projective geometry

Geometry

Hodge theory and Lagrangian planes on generalized Kummer fourfolds

Brendan, H. & Tschinkel, Y., Jan 2013, In : Moscow Mathematical Journal. 13, 1, p. 33-56 24 p.

Research output: Contribution to journal › Article

Hodge Theory

Projective plane

Submanifolds

Homology

Intersection

Integral points of bounded height on compactifications of semi-simple groups

Takloo-Bighash, R. & Tschinkel, Y., Oct 2013, In : American Journal of Mathematics. 135, 5, p. 1433-1448 16 p.

Research output: Contribution to journal › Article

Integral Points

Semisimple Groups

Compactification

Asymptotic distribution

Partial

On the moduli space of degree 4 Del Pezzo surfaces

Tschinkel, Y., Hassett, B. & Kresch, A., 2013, (Accepted/In press) Mukai Festschrift: Advanced Studies in Pure Mathematics. 37 p. In press

Research output: Chapter in Book/Report/Conference proceeding › Chapter (peer-reviewed)

Preface

Bogomolov, F., Hassett, B. & Tschinkel, Y., Jan 1 2013, In : Unknown Journal. p. 1-319 319 p.

Research output: Contribution to journal › Article

2012

Characterizing projective spaces on deformations of Hilbert schemes of K3 surfaces

Harvey, D., Hassett, B. & Tschinkel, Y., Feb 2012, In : Communications on Pure and Applied Mathematics. 65, 2, p. 264-286 23 p.

Research output: Contribution to journal › Article

Hilbert Scheme

K3 Surfaces

Projective Space

Torsional stress

Homology

Height zeta functions of equivariant compactifications of semi-direct products of algebraic groups

Tschinkel, Y. & Tanimoto, S., 2012, In : Contemporary Mathematics. 566, p. 119-157

Research output: Contribution to journal › Article

Integral points of bounded height on partial equivariant compactifications of vector groups

Chambert-Loir, A. & Tschinkel, Y., Dec 1 2012, In : Duke Mathematical Journal. 161, 15, p. 2799-2836 38 p.

Research output: Contribution to journal › Article

Integral Points

Compactification

Asymptotic Formula

Equivariant

Partial

Introduction to birational anabelian geometry

Bogomolov, F. & Tschinkel, Y., 2012, Current developments in algebraic geometry. Cambridge: Cambridge University Press, p. 17-63 (Publications of the Research Institute for Mathematical Sciences; vol. 59).

Research output: Chapter in Book/Report/Conference proceeding › Chapter (peer-reviewed)

Spaces of sections of quadric surface fibrations over curves

Tschinkel, Y. & Hassett, B., 2012, In : Contemporary Mathematics. 564, p. 227-249

Research output: Contribution to journal › Article

2011

Constructing rational curves on K3 surfaces

Bogomolov, F., Hassett, B. & Tschinkel, Y., Apr 15 2011, In : Duke Mathematical Journal. 157, 3, p. 535-550 16 p.

Research output: Contribution to journal › Article

K3 Surfaces

Rational Curves

Picard Group

Galois field

Modulo

Editorial Material

Katzarkov, L., Pantev, T., Tschinkel, Y. & Zarhin, Y., Oct 2011, In : Central European Journal of Mathematics. 9, 5, p. 935 1 p.

Research output: Contribution to journal › Article

Effectivity of Brauer-Manin obstructions on surfaces

Kresch, A. & Tschinkel, Y., Mar 20 2011, In : Advances in Mathematics. 226, 5, p. 4131-4144 14 p.

Research output: Contribution to journal › Article

Obstruction

Azumaya Algebra

Hasse Principle

Weak Approximation

Brauer Group

Reconstruction of higher-dimensional function fields

Bogomolov, F. & Tschinkel, Y., 2011, In : Moscow Mathematical Journal. 11, 2, p. 185-204 20 p.

Research output: Contribution to journal › Article

Lower Central Series

Galois group

Function Fields

Modulo

Quotient

2010

A Torelli theorem for curves over finite fields

Bogomolov, F., Korotiaev, M. & Tschinkel, Y., Jan 2010, In : Pure and Applied Mathematics Quarterly. 6, 1, p. 245-294 50 p.

Research output: Contribution to journal › Article

Galois field

Curve

Theorem

Context

Cohomological and geometric approaches to rationality problems: New perspectives

Bogomolov, F. (ed.) & Tschinkel, Y. (ed.), 2010, Boston: Birkhäuser Verlag. 311 p. (Progress in mathematics; vol. v. 282)

Research output: Book/Report › Book

Flops on holomorphic symplectic fourfolds and determinantal cubic hypersurfaces

Hassett, B. & Tschinkel, Y., Jan 2010, In : Journal of the Institute of Mathematics of Jussieu. 9, 1, p. 125-153 29 p.

Research output: Contribution to journal › Article

Hypersurface

Cone

Automorphism

Decompose

Line

Igusa integrals and volume asymptotics in analytic and adelic geometry

Tschinkel, Y. & Chambert-Loir, A., 2010, In : Confluentes Mathematici. 2, 3, p. 351-429

Research output: Contribution to journal › Article

Integral points of bounded height on toric varieties

Tschinkel, Y. & Chambert-Loir, A., 2010, 28 p.

Research output: Other contribution

Intersection numbers of extremal rays on holomorphic symplectic varieties

Hassett, B. & Tschinkel, Y., Sep 2010, In : Asian Journal of Mathematics. 14, 3, p. 303-322 20 p.

Research output: Contribution to journal › Article

Intersection number

Half line

Unramified cohomology of finite groups of Lie type

Bogomolov, F., Petrov, T. & Tschinkel, Y., 2010, Progress in Mathematics. Springer Basel, Vol. 282. p. 55-73 19 p. (Progress in Mathematics; vol. 282).

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Finite Groups of Lie Type

Cohomology

2009

Algebra, arithmetic, and geometry: In honor of Y.I. Manin

Tschinkel, Y. (ed.), Zarhin, Y. (ed.) & Manin, IU. I. (ed.), 2009, Boston, [Mass.]: Birkhäuser Verlag. (Progress in mathematics; vol. 269, 270)

Research output: Book/Report › Book

Arithmetic geometry

Tschinkel, Y. (ed.), Darmora, S. (ed.) & Hassett, B. (ed.), 2009, Proceedings of the Clay Summer School Gotteingen 2006. AMS, (CMI Proceedings series).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Co-fibered products of algebraic curves

Bogomolov, F. & Tschinkel, Y., 2009, In : Central European Journal of Mathematics. 7, 3, p. 382-386 5 p.

Research output: Contribution to journal › Article

Algebraic curve