Institute of Mathematics

Person

Prof. Dr. Andrew Kresch

Institut für Mathematik
Universität Zürich
Winterthurerstrasse 190
CH-8057 Zürich

E-Mail:
Phone: +41 44 635 58 82
Fax: +41 44 635 57 06
Office: Y27K38
Field of Research:
Algebraische Geometrie
Working group:
Secretary:
E-Mail:
Phone:
Grit Schütze

+41 44 635 58 00

Research

The program farsta computes Gromov-Witten invariants of algebraic varieties: farsta-1.1.tar.gz
(Patch by Felix Janda for Linux systems; application: patch < farsta.patch)

Magma scripts on del Pezzo surfaces of degree 2.

For the computations in the paper “On the spaces generated by vectors with coordinates in incomplete residue systems”: first magma scriptsecond magma script
Fall 23

Publications

A. Kresch, Yu. Tschinkel
Unramified Brauer group of quotient spaces by finite groups
preprint PDF  

A. Kresch, Yu. Tschinkel
Birational geometry of Deligne-Mumford stacks
preprint PDF  

A. Kresch, S. Mathur
Formal GAGA for gerbes
preprint PDF  

A. Kresch, Yu. Tschinkel
Burnside groups and orbifold invariants of birational maps
preprint PDF  

A. Kresch, Yu. Tschinkel
Equivariant Burnside groups: structure and operations
preprint PDF  

A. Kresch, Yu. Tschinkel
Cohomology of finite subgroups of the plane Cremona group
Algebraic Geom. and Physics, to appear PDF  

A. Kresch, Yu. Tschinkel
Equivariant Burnside groups and toric varieties
Rend. Circ. Mat. Palermo 72 (2023), 3013-3039 PDF  

B. Hassett, A. Kresch, Yu. Tschinkel
Stable rationality in smooth families of threefolds
Duke Math. J. 172 (2023), 1145-1172 PDF  

A. Kresch, Yu. Tschinkel
Fibrations in sextic del Pezzo surfaces with mild singularities
Rend. Semin. Mat. Univ. Padova 148 (2022), 65-82 PDF  

A. Kresch, Yu. Tschinkel
Equivariant Burnside groups and representation theory
Selecta Math. 28 (2022), Article No. 81 PDF  

A. Kresch, Yu. Tschinkel
Equivariant birational types and Burnside volume
Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 23 (2022), 1013-1052 PDF  

B. Hassett, A. Kresch, Yu. Tschinkel
Symbols and equivariant birational geometry in small dimensions
in Rationality of Varieties, Progr. Math. 342, Birkhäuser, Cham, 2021, pp. 201-236 PDF  

A. Kresch, Yu. Tschinkel
Brauer groups of involution surface bundles
Pure Appl. Math. Q. 17 (2021), 649-669 PDF  

A. Kresch, Yu. Tschinkel
Birational types of algebraic orbifolds
Mat. Sb. 212:3 (2021), 54-67 PDF  

A. Kresch, Yu. Tschinkel
Arithmetic properties of equivariant birational types
Res. Number Theory 7 (2021), Article No. 27 PDF  

A. Kresch
Descent of vector bundles under wildly ramified extensions
Eur. J. Math. 6 (2020), 1255-1263 PDF  

A. Kresch, Yu. Tschinkel
Involution surface bundles over surfaces
Math. Zeitschrift 296 (2020), 1081-1100 PDF  

A. Kresch, Yu. Tschinkel
Stable rationality of Brauer-Severi surface bundles
Manuscripta Math. 161 (2020), 1-14 PDF  

A. Kresch, Yu. Tschinkel
Models of Brauer-Severi surface bundles
Moscow Math. J. 19 (2019), 549-595 PDF  

A. Kresch, Yu. Tschinkel
Models of triple covers
Mat. Zametki 105 (2019), 798-800 PDF  

A. Kresch
Destackification with restricted root operations
Eur. J. Math. 4 (2018), 1421-1432 PDF  

A. Kresch
On the spaces generated by vectors with coordinates in incomplete residue systems
Res. Math. Sci. 5 (2018), Article No. 36 PDF  

A. S. Buch, A. Kresch, H. Tamvakis
A Giambelli formula for isotropic Grassmannians
Selecta Math. 23 (2017), 869-914 PDF  

J. Alper, A. Kresch
Equivariant versal deformations of semistable curves
Michigan Math. J. 65 (2016), 227-250 PDF  

B. Hassett, A. Kresch, Yu. Tschinkel
Stable rationality and conic bundles
Math. Ann. 365 (2016), 1201-1217 PDF  

A. S. Buch, A. Kresch, K. Purbhoo, H. Tamvakis
The puzzle conjecture for the cohomology of two-step flag manifolds
J. Algebraic Combin. 44 (2016), 973-1007 PDF  

B. Hassett, A. Kresch, Yu. Tschinkel
On the moduli of degree 4 Del Pezzo surfaces
in Development of Moduli Theory (Kyoto 2013), Adv. Stud. Pure Math. 69, Math. Soc. Japan, Tokyo, 2016, pp. 349-386 PDF  

A. S. Buch, A. Kresch, H. Tamvakis
A Giambelli formula for even orthogonal Grassmannians
J. Reine Angew. Math. 708 (2015), 17-48 PDF  

B. Kim, A. Kresch, Y.-G. Oh
A compactification of the space of maps from curves
Trans. Amer. Math. Soc. 366 (2014), 51-74 PDF  

B. Hassett, A. Kresch, Yu. Tschinkel
Effective computation of Picard groups and Brauer-Manin obstructions of degree two K3 surfaces over number fields
Rend. Circ. Mat. Palermo 62 (2013), 137-151 PDF  

A. Kresch
Flattening stratification and the stack of partial stabilizations of prestable curves
Bull. London Math. Soc. 45 (2013), 93-102 PDF  

A. S. Buch, A. Kresch, H. Tamvakis
Quantum Giambelli formulas for isotropic Grassmannians
Math. Ann. 354 (2012), 801-812 PDF  

A. Kresch, Yu. Tschinkel
Effectivity of Brauer-Manin obstructions on surfaces
Adv. Math. 226 (2011), 4131-4144 PDF  

A. Kresch
CW complexes for complex algebraic surfaces
Experiment. Math. 19 (2010), 413-419 PDF  

A. S. Buch, A. Kresch, H. Tamvakis
Quantum Pieri rules for isotropic Grassmannians
Invent. Math. 178 (2009), 345-405 PDF  

A. Kresch
On the geometry of Deligne-Mumford stacks
in Algebraic Geometry (Seattle, 2005), Proc. Sympos. Pure Math. 80, Part 1, Amer. Math. Soc., Providence, RI, 2009, pp. 259-271 PDF  

A. Kresch, Yu. Tschinkel
Two examples of Brauer-Manin obstruction to integral points
Bull. London Math. Soc. 40 (2008), 995-1001. PDF  

A. Kresch, Yu. Tschinkel
Effectivity of Brauer-Manin obstructions
Adv. Math. 218 (2008), 1-27 PDF  

A. S. Buch, A. Kresch, M. Shimozono, H. Tamvakis, A. Yong
Stable Grothendieck polynomials and K-theoretic factor sequences
Math. Ann. 340 (2008), 359-382 PDF  

A. Kresch
Flag varieties and Schubert calculus
in Algebraic Groups (Proc. Summer School, Göttingen, 2005), Universitätsverlag Göttingen, Göttingen, 2007, pp. 73-86. PDF  

A. S. Buch, A. Kresch, H. Tamvakis, A. Yong
Grothendieck polynomials and quiver formulas
Amer. J. Math. 127 (2005), 551-567 PDF  

A. Kresch, Yu. Tschinkel
On the arithmetic of del Pezzo surfaces of degree 2
Proc. London Math. Soc. (3) 89 (2004), 545-569 PDF  

A. S. Buch, A. Kresch, H. Tamvakis
Littlewood-Richardson rules for Grassmannians
Adv. Math. 185 (2004), 80-90 PDF  

N. D. Elkies, E. W. Howe, A. Kresch, B. Poonen, J. L. Wetherell, M. E. Zieve
Curves of every genus with many points, II: Asymptotically good families
Duke Math. J. 122 (2004), 399-422 PDF  

A. S. Buch, A. Kresch, H. Tamvakis, A. Yong
Schubert polynomials and quiver formulas
Duke Math. J. 122 (2004), 125-143 PDF  

A. Kresch, A. Vistoli
On coverings of Deligne-Mumford stacks and surjectivity of the Brauer map
Bull. London Math. Soc. 36 (2004), 188-192 PDF  

A. Kresch, H. Tamvakis
Quantum cohomology of orthogonal Grassmannians
Compositio Math. 140 (2004), 482-500 PDF  

A. S. Buch, A. Kresch, H. Tamvakis
Gromov-Witten invariants on Grassmannians
J. Amer. Math. Soc. 16 (2003), 901-915 PDF  

A. Kresch, H. Tamvakis
Quantum cohomology of the Lagrangian Grassmannian
J. Algebraic Geom. 12 (2003), 777-810 PDF  

B. Kim, A. Kresch, T. Pantev
Functoriality in intersection theory and a conjecture of Cox, Katz, and Lee
J. Pure Appl. Algebra 179 (2003), 127-136 PDF  

A. Kresch
Hodge-theoretic obstruction to the existence of quaternion algebras
Bull. London Math. Soc. 35 (2003), 109-116 PDF  

A. Kresch, Yu. Tschinkel
Integral points on punctured abelian surfaces
in Algorithmic Number Theory ANTS-V (Sydney, 2002), Lect. Notes in Comput. Sci. 2369, Springer-Verlag, Berlin, 2002, pp. 198-204 PDF  

A. Kresch, H. Tamvakis
Double Schubert polynomials and degeneracy loci for the classical groups
Ann. Inst. Fourier (Grenoble) 52 (2002), 1681-1727 PDF  

A. Kresch, J. L. Wetherell, M. E. Zieve
Curves of every genus with many points, I: Abelian and toric families
J. Algebra 250 (2002), 353-370 PDF  

A. Kresch, H. Tamvakis
Standard conjectures for the arithmetic Grassmannian G(2,N) and Racah polynomials
Duke Math J. 110 (2001), 359-376 PDF  

D. Edidin, B. Hassett, A. Kresch, A. Vistoli
Brauer groups and quotient stacks
Amer. J. Math. 123 (2001), 761-777 PDF  

A. Kresch
Gromov-Witten invariants of a class of toric varieties
Michigan Math. J. 48 (2000), 369-391 PDF  

A. Kresch
Cycle groups for Artin stacks
Invent. Math. 138 (1999), 495-536 PDF  

A. Kresch
Canonical rational equivalence of intersections of divisors
Invent. Math. 136 (1999), 483-496 PDF  

A. Kresch
Associativity relations in quantum cohomology
Adv. Math. 142 (1999), 151-169 PDF