Downloadable research papers

(For downloadable expository writing go to the relevant webpage.) 

Conformal blocks and the cohomology of configuration spaces of curves, 57 p. (Dec. 2021).

Monodromy and period map of the Winger pencil (with Yunpeng Zi), 20 p. (Sept. 2021)

Arithmetic representations of mapping class groups, 13 p. (Aug. 2021).

Characteristic forms for holomorphic families of local systems (with Indranil Biswas), 22 p. (July 2021).

The Nielsen realization problem for K3 surfaces (with Benson Farb), 38 p. (April 2021).

Remarkable polydifferentials on  the configuration space of a compact Riemann surface, 7 p. (March 2021).

Torelli group action on the configuration space of a surface, 7 p., (Aug, 2020), to appear in the J. of Topology and Analysis.

Lifting Chern classes by means of Ekedahl-Oort strata (with Gerard van der Geer), 11 p. (Dec. 2019), Tunisian J. of Math. 3, 469-480.

Geometry of the Wiman-Edge pencil and the Wiman curve (with Benson Farb),  Geometriae Dedicata 208, 197–220 (2020).

Arithmeticity of the monodromy of the Wiman-Edge pencil (with Benson Farb), 28 p. (Nov. 2019), to appear in Ann. Inst. Fourier.

Geometry of the Wiman–Edge pencil, I: algebro-geometric aspects (with Igor Dolgachev and Benson Farb), Eur. J. Math. 4 (2018), 879–930.  

Deforming a canonical curve inside a quadric (with Marco Boggi), Intern. Math. Res. Notices, 2020, Issue 2, January 2020, Pages 367–377, https://doi.org/10.1093/imrn/rny027

Goresky-Pardon lifts of Chern classes and some Tate extensions, Compositio Math. 153 (2017), 1349-1371.

The homotopy type of the Baily-Borel and allied compactifications (with Jiaming Chen), Homology, Homotopy and Applications 23 (2021), 95-119, http://dx.doi.org/10.4310/HHA.2021.v23.n2.a6

The stable cohomology of the Satake compactification of A_g (with Jiaming Chen), Geometry and Topology 21 (2017),  2231-2241. 

Discrete automorphism groups of convex cones of finite typeCompositio Math. 150 (2014), 1939-1962.

The fine structure of the moduli space of abelian differentials in genus 3 (with Gabriele Mondello), Geom. Dedicata 169 (2014), 109–128.

From WZW models to modular functors, Handbook of moduli. Vol. II, 427–466, Adv. Lect. Math. (ALM) 25, Int. Press, Somerville, MA, 2013

Connectivity of complexes of separating curvesGroups Geom. Dyn. 7 (2013), 443–450.

The KZ system via polydifferentials. Arrangements of hyperplanes—Sapporo 2009, 189–231, Adv. Stud. Pure Math. 62, Math. Soc. Japan, Tokyo, 2012.

Spherical complexes attached to symplectic lattices (with Wilberd van der Kallen), Geom. Dedicata 152 (2011), 197–211.

Hyperbolic structures and root systems (with Gert Heckman), in:  Casimir force, Casimir operators and the Riemann hypothesis, 211–228, Walter de Gruyter, Berlin, 2010.

Fermat varieties and the periods of some hypersurfaces, Algebraic and arithmetic structures of moduli spaces (Sapporo 2007), 47–67, Adv. Stud. Pure Math. 58, Math. Soc. Japan, Tokyo, 2010. 

On the unitary nature of abelian conformal blocks (with Alex Boer), J. Geom. Phys. 60 (2010), 205–218.

Del Pezzo moduli via root systems (with Elisabetta Colombo and Bert van Geemen), in:  Algebra, arithmetic, and geometry: in honor of Yu. I. Manin. Vol. I, 291–337, Progr. Math. 269, Birkhäuser Boston, Inc., Boston, MA, 2009.

The period map for cubic fourfolds, Invent. Math. 177 (2009), 213–233. 

Unitarity of SL(2)-conformal blocks in genus zero, J. Geom. Phys. 59 (2009), 654–662.

A perfect stratification of Mg for g≤5 (with Claudio Fontanari) Geom. Dedicata 136 (2008), 133–143.

On period maps that are open embeddings (with Rogier Swierstra),  J. Reine Angew. Math. 617 (2008), 169–192.

Artin groups and the fundamental groups of some moduli spaces, J. Topol. 1 (2008), 187–216. 

The period map for cubic threefolds (with Rogier Swierstra), Compositio. Math. 143 (2007), 1037–1049.

Invariants of quartic plane curves as automorphic forms, Algebraic geometry, 107–120, Contemp. Math. 422, Amer. Math. Soc., Providence, RI, 2007. 

On the geometry of the Calogero-Moser system (with Wim Couwenberg and Gert Heckman),  Indag. Math. (N.S.) 16 (2005), 443–459. 

Geometric structures on the complement of a projective arrangement (with Wim Couwenberg and Gert Heckman), Publ. Math. Inst. Hautes Études Sci. 101 (2005), 69–161.

Compactifications defined by arrangements. II, Locally symmetric varieties of type IV. Duke Math. J. 119 (2003), 527–588. 

Compactifications defined by arrangements. I, The ball quotient case. Duke Math. J. 118 (2003), 151–187.

Correspondences between moduli spaces of curves, in Moduli of curves and abelian varieties, 131–150, Aspects Math., E33, Vieweg, Braunschweig, 1999. 

A Lie algebra attached to a projective variety (with Valery Lunts),  Invent. Math. 129 (1997), 361–412.

Prym representations of mapping class groups, Geom. Dedicata 64 (1997), 69–83.

Stable cohomology of the mapping class group with symplectic coefficients and of the universal Abel-Jacobi map, J. Algebraic Geom. 5 (1996), 135–150.

Cellular decompositions of compactified moduli spaces of pointed curves, The moduli space of curves (Texel Island, 1994), 369–400, Progr. Math. 129, Birkhäuser Boston, Boston, MA, 1995.

On the tautological ring of Mg. Invent. Math. 121 (1995), 411–419.

Smooth Deligne-Mumford compactifications by means of Prym level structures, J. Algebraic Geom. 3 (1994), 283–293.

Cohomology of M_3 and M_{3,1}, in: Mapping class groups and moduli spaces of Riemann surfaces (Göttingen, 1991/Seattle, WA, 1991), 205–228, Contemp. Math. 150, Amer. Math. Soc., Providence, RI, 1993. For a correction see 
The Hodge polynomial of Mbar_{3,1} (with Ezra Getzler)