Valery Alexeev


Department of Mathematics
University of Georgia
Athens GA 30602, USA


Papers and preprints

Divisors on Burniat surfaces, Advanced Studies in Pure Mathematics (Mathematical Society of Japan), to appear.

Moduli of weighted hyperplane arrangements, with applications, Notes for the May 2013 Barcelona Advanced course "Compactifying Moduli spaces", version 11-26-13.

(with Rita Pardini) On the existence of ramified abelian covers, Rendiconti del Seminario Matematico Universita e Politecnico di Torino, to appear.

(with Dmitri Orlov) Derived categories of Burniat surfaces and exceptional collections, Math. Annalen, 357, issue 2 (2013), 743-759.

(with Alexander Borisov) On the log discrepancies in Mori contractions, Proc. Amer. Math. Soc., to appear.

(with Christopher Hacon) Non-rational centers of log canonical singularities, J. Algebra, 369 (2012), 1-15.

(with Ryan Livingson, Joe Tenini, et al.) Extended Torelli map to the Igusa blowup in genus 6, 7, and 8. (long version here.), Experimental Mathematics, 21(2), 2012, 193-203.

(with Rita Pardini) Non-normal abelian covers, Compositio Mathematica, 148, no. 4 (2012), 1051-1084.

(with Adrian Brunyate) Extending Torelli map to toroidal compactifications of Siegel space, Inventiones Mathematicae, 188 (2012), issue 1, 175-196.

(with Angela Gibney and David Swinarski) Conformal blocks divisors on M0,n from sl(2), Proc. Edinburgh Math. Soc., 57 (2014), 7-30.

(with Rita Pardini) Explicit compactifications of moduli spaces of Campedelli and Burniat surfaces: color version, black-and-white version.

(with David Swinarski) Nef divisors on M0,n from GIT, Geometry and Arithmetic, 2012, European Math. Soc., EMS Congress Reports, pp. 1-22.

Weighted grassmannians and stable hyperplane arrangements (updated 6/19/08)

Higher-dimensional analogues of stable curves,
Proceedings of Madrid ICM2006, 2 (2006), 515-536, Eur. Math. Soc. Pub. House.

(with Michael Guy) Moduli of weighted stable maps and their gravitational descendants, Journal of the Institute of Mathematics of Jussieu, 7 (2008), no.3, 425-456.

Limits of stable pairs, Pure and Applied Math Quaterly, 4 (2008), no.3, 767-783.

(with Christopher Hacon and Yujiro Kawamata) Termination of (many) 4-dimensional log flips
(successor to "A note on termination of 4-dimensional flips" below)
Inventiones Mathematicae, 168 (2007), 433-448.

(with Viacheslav V. Nikulin) Del Pezzo and K3 surfaces,
Memoirs of the Mathematical Society of Japan, 15 (2006), x+149pp.

(with Allen Knutson) Complete moduli of branchvarieties, Jour. f.d. Reine Angew. Mathematik (Crelle's Journal), 639 (2010), 29-71.

(with Michel Brion) Stable spherical varieties and their moduli
International Math. Research Papers, vol. 2006 (2006), Article ID 46293, 57 pages.

Compactified jacobians and Torelli map, Publ. RIMS, Kyoto Univ. 40 (2004), 1241-1265. (40-year RIMS anniversary issue). (Here is a local copy.)

A note on termination of 4-dimensional flips (6/8/2004)

(with Viacheslav V. Nikulin) Classification of log del Pezzo surfaces of index <=2

(with Michel Brion) Toric degenerations of spherical varieties, Selecta Mathematica 10 (2004), 1-26.

(with Ludmil Katzarkov) On K-stability of reductive varieties, Geometric and Functional Analysis GAFA 15:2 (2005), 297-310.

(with Michel Brion) Moduli of affine schemes with reductive group action
Journal of Algebraic Geometry 14 (2005), 83-117.

(with Michel Brion) Boundedness of spherical Fano varieties, Proceedings of "The Fano conference" Turin Sept. 2002, pp. 69-80 (2004).

(with Michel Brion) Stable reductive varieties I: Affine varieties, Inventiones Math. 157/2 (2004), 224-274.

(with Michel Brion) Stable reductive varieties II: Projective case, Advances of Math. 184/2 (2004), 380-408.

Complete moduli in the presence of semiabelian group action, Annals of Math. 155 (2002), 611-708.

(with Christina Birkenhake and Klaus Hulek) Degenerations of Prym varieties, Jour. f.d. Reine Angew. Mathematik (Crelle's Journal) 553 (2002), 73-116.

(with Shigefumi Mori) Bounding singular surfaces of general type
In "Algebra, Arithmetic and Geometry with Applications", ed. by Christensen et al, Springer-Verlag (2003), 143-174.

(with Iku Nakamura) On Mumford's construction of degenerating abelian varieties, Tohoku Mathematical Journal 51(1999), 399-420.

On extra components in the functorial compactification of Ag, Moduli of Abelian Varieties (Texel island) (K.Faber, G. van der Geer, and F.Oort, eds.), Progress in Mathematics 195, Birkhauser, Boston, 2001, 1-9.

Log canonical singularities and complete moduli of stable pairs, arXiv alg-geom/9608013.

Compactified jacobians, arXiv alg-geom/9608012.

Moduli spaces Mg,n(W) for surfaces, Proceedings of the international conference held in Trento, Italy, June 1994. Walter de Gruyter, 1996.

On general elephants of Q-Fano 3-folds, Compositio Math. 90 (1994), 91-116.

Boundedness and K2 for log surfaces, Internat. J. Math. 5 (1994), no. 6., 779-810.

Two two-dimensional terminations, Duke Math. J. 69 (1993), no.3, 527-545.

Classification of log canonical surface singularities: Arithmetical proof. In: Flips and abundance for algebraic threefolds, Asterisque, vol. 211, 1992, 47-58.

Ample Weil divisors on K3 surfaces with Du Val singularities, Duke Math. J. 64 (1991), no.3., 617-624.

Theorems about good divisors on log Fano varieties (case of index r > n-2), Algebraic Geometry, Chicago (1989), Lecture Notes in Math., vol 1479, Springer-Verlag, 1991, 1-9.

Fractional indices of log del Pezzo surfaces, Math. USSR-Izv., 33 (1989), 613-629. Correction.

(with V.V. Nikulin) Classification of del Pezzo surfaces with log terminal singularities of index ≤2 and involutions on K3 surfaces, Soviet Math. Dokl. 39 (1989), 525-528.

(with I. Kolpakov) On quotient surfaces P2 by a finite group, Uspekhi Mat. Nauk 43 (1988), no.5, 171-172.

(with V.V. Niulin) Classification of del Pezzo surfaces with log terminal singularities of index ≤2, involutions on K3 surfaces and reflection groups in Lobachevsky spaces, Reports in Mathematics and its Applications 2 (1988), no.2, 51-150.

Rationality conditions for three-dimensional varieties with a pencil of del Pezzo surfaces of degree 4, Math. Notes 41 (1987), 408-411.


Books edited

(with Arnaud Beauville, C. Herbert Clemens, Elham Izadi) Curves and Abelian Varieties: International conference March 30-April 2, 2007, University of Georgia, Athens. Contemporary Mathematics, American Math. Soc., Vol. 465 (2008), 270 pp.

(with Angela Gibney, Elham Izadi, Eduard Looijenga, János Kollár) Compact Moduli and Vector Bundles. Proceedings of the 2010 conference at the University of Georgia, Athens. Contemporary Mathematics, American Math. Soc., 564 (2012), 249 pp.


Some conferences I coorganized

March 30 - April 3, 2007: Curves and abelian varieties, University of Georgia, Athens, GA

October 21-24, 2010: Compact moduli and vector bundles, University of Georgia, Athens, GA

May 21 - June 1, 2012: UGA school and conference on algebraic geometry, Athens, GA

October 18-20, 2013: Georgia Algebraic Geometry Symposium 2013, Athens, GA

October 17-19, 2014: Georgia Algebraic Geometry Symposium 2014, Athens, GA



My students

Vitaly Vologodsky, PhD 2003, The extended Jacobi and Prym maps

Tawanda Gwena, PhD 2004, Degenerations of Prym varieties and Cubic threefold

Michael Guy, PhD 2007, Moduli of Weighted Stable Maps and Their Gravitational Descendants

Peter Petrov, PhD 2007, Nash problem on spaces of arcs

Joe Rusinko, PhD 2007, Equivalence of Mirror Families Constructed from Toric Degenerations of Flag Varieties

Jaeho Shin, PhD 2013, The reduction map for the moduli spaces of weighted hyperplane arrangements

Xiaoyan (Shannon) Hu, PhD 2014, The compactifications of moduli spaces of Burniat surfaces with 2≤K2≤5

Joe Tenini, PhD 2014, Results on an Extended Torelli Map and Singularities of Degenerate Abelian Varieties

Adrian Brunyate

Luca Schaffler


Conferences, talks, etc

(2013)

May 4-9: K3 surfaces and their moduli, Schiemonnikoog island, the Netherlands

June 2-30: Higher school of mathematics, Moscow, Russia

July 14-18: Complex geometry and algebraic geometry, Beijing International Center of Math Research, Beijing, China

November 10-14: K3, Enriques surfaces and related topics, Nagoya University, Japan

Teaching

In 2001-12 together with Ted Shifrin and Boris Alexeev I coorganized the annual UGA Mathematical Competition for High School Students.

Recipient of a 2009 Sandy Beaver Excellence in Teaching Award from the UGA Franklin College of Arts and Sciences.



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