Department
of Mathematics

University of Georgia

Athens GA 30602, USA

## Papers and preprints

(with Wenfei Liu)
Open surfaces of small volume.

(with Alan Thompson)
Modular compactification of moduli of K3 surfaces of degree 2,
Manuscript in preparation, Preliminary version.

(with Ron Donagi, Gavril Farkas, Elham Izadi, Angela Ortega)
The uniformization of the moduli space of principally polarized abelian 6-folds.

Divisors on Burniat surfaces,
Advanced Studies in Pure Mathematics (Mathematical Society of Japan), **69** (2016), pp. 287-302.

Moduli of weighted hyperplane arrangements,
Advanced Cources in Mathematics - CRM Barcelona, Springer Basel, 2015.

(with Rita Pardini)
On the existence of ramified
abelian covers, Rend. Sem. Mat. Univ. Politec. Torino **71**, 3-4 (2013), 307-315.

(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., **142** (2014), no. 11, 3687-3694.

(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)
Higher level sl(2) conformal
blocks divisors on
M_{0,n}, 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
M_{0,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 A*_{g}, 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 M_{g,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 K^{2} 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 P^{2} 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

March 3-5, 2017:
Georgia Algebraic Geometry Symposium 2017, 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≤K*^{2}≤5

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

Adrian Brunyate, PhD 2015,
*A Modular Compactification of the Space of Elliptic K3 Surfaces*

Luca Schaffler

## Conferences, talks, etc

(2014)
(2015)

## 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.

Mandatory
disclaimer: The contents and opinions expressed on this Web
page do not necessarily reflect the views of nor are they endorsed by
the University of Georgia or the University System of Georgia.