Papers, preprints, and talk notes

This is a rather up-to-date list of my papers and preprints, in reverse chronological order of writing (not always the same as posting). You can also check the listings in the arXiv, and the reviews in Mathscinet or Zentralblatt.

I have collaborated with: Matt Bainbridge, Sebastian Casalaina-Martin, Dawei Chen, Giulio Codogni, Emily Clader, Fabien Cléry, Francesco Dalla Piazza, Mathieu Dutour Sikirić, Alessio Fiorentino, Cord Erdenberger, Gavril Farkas, Gerard van der Geer, Quentin Gendron, Klaus Hulek, Felix Janda, Igor Krichever, Radu Laza, David Lehavi, Martin Möller, Chaya Norton, Sara Perna, Riccardo Salvati Manni, Edoardo Sernesi, Orsola Tommasi, Alessandro Verra, Dmitry Zakharov.

46. (with H. Farkas, R. Salvati Manni) An explicit solution to the weak Schottky problem.
45. (with I. Krichever, C. Norton) Real-normalized differentials: limits on stable curves.
44. (with K. Hulek, O. Tommasi) Stable Betti numbers of (partial) toroidal compactifications of the moduli space of abelian varieties (with an appendix by M. Dutour Sikirić).
    Proceedings in honour of Nigel Hitchin's 70th birthday, Oxford University Press, to appear.
43. (with M. Bainbridge, D. Chen, Q. Gendron, M. Möller) Strata of k-differentials.
42. (with G. Codogni, E. Sernesi) The degree of the Gauss map of the theta divisor.
    Algebra and Number Theory 11 (2017), 983-1001.
41. (with E. Clader, F. Janda, D. Zakharov) Powers of the theta divisor and relations in the tautological ring.
    International Mathematics Research Notices, to appear.
40. (with M. Bainbridge, D. Chen, Q. Gendron, M. Möller) Compactification of strata of abelian differentials.
39. (with K. Hulek) The intersection cohomology of the Satake compactification of Ag for g≤4.
    Mathematische Annalen 369 (2017) 3-4, 1353-1381.
38. (with S. Casalaina-Martin, K. Hulek, R. Laza) Complete moduli of cubic threefolds and their intermediate Jacobians.
37. (with M. Möller) Explicit formulas for infinitely many Shimura curves in genus 4.
    Asian Journal of Mathematics, special issue dedicated to Ngaimining Mok's 60th birthday, to appear.
36. (with F. Dalla Piazza, A. Fiorentino, S. Perna, R. Salvati Manni) Vector-valued modular forms and the Gauss map.
    Documenta Mathematica 22 (2017), 1063-1080.
35. (with S. Casalaina-Martin, K. Hulek, R. Laza) Extending the Prym map to toroidal compactifications of the moduli space of abelian varieties (with an appendix by M. Dutour Sikirić)
    Journal of European Mathematical Society 19 (2017) 3, 659-723.
34. (with M. Möller) Shimura curves within the locus of genus 3 hyperelliptic curves.
    International Mathematics Research Notices 2016 (2016) 6, 1603-1639.
33. (with K. Hulek, O. Tommasi) Stable cohomology of the perfect cone toroidal compactification of the moduli space of abelian varieties.
   Journal fur die reine und angewandte Mathematik (Crelle's Journal), to appear.
32. (with F. Cléry, G. van der Geer) Siegel modular forms of genus 2 and level 2 (with an appendix by S. Mukai).
   International Journal of Mathematics 26 (2015) 5, 51pp.
31. (with R. Salvati Manni) On the Coble quartic.
    American Journal of Mathematics 137 (2015) 3, 765-790.
30. (with D. Zakharov) The zero section of the universal semiabelian variety, and the double ramification cycle.
    Duke Mathematical Journal 163 (2014) 5, 953-982.
29. (with D. Zakharov) The double ramification cycle and the theta divisor.
    Proceedings of the American Mathematical Society 142 (2014) 12, 4053-4064.
28. (with K. Hulek) Geometry of theta divisors - a survey.
    Clay Mathematics Proceedings 18 (A Celebration of Algebraic Geometry, on the occasion of Joe Harris' 60th birthday), 361-390.
27. (with G. Farkas, R. Salvati Manni, A. Verra ) Singularities of theta divisors and the geometry of A5.
    Journal of European Mathematical Society 16 (2014) 9, 1817-1848.
26. (with I. Krichever) Foliations on the moduli space of curves, vanishing in cohomology, and Calogero-Moser curves.
25. (with R. Salvati Manni) The Prym map on divisors, and the slope of A5 (with an appendix by K. Hulek).
    International Mathematics Research Notices 2014 (2014) 24, 6645-6660.
24. (with K. Hulek) The class of the locus of intermediate Jacobians of cubic threefolds.
    Inventiones Mathematicae 190 (2012) 1, 119-168.
23. (with K. Hulek) Principally polarized semi-abelic varieties of small torus rank, and the Andreotti-Mayer loci.
    PAMQ (Viehweg memorial issue) 7 (2011) 4, 1309-1360.
22. (with R. Salvati Manni) The Scorza correspondence in genus 3.
    Manuscripta Mathematica 141 (2013) 1-2, 111-124.
21. The Schottky problem.
    Current Developments in Algebraic Geometry, 129-164, MSRI Publications 59, Cambridge Univ. Press (2012).
20. (with I. Krichever) The universal Whitham hierarchy and the geometry of the moduli space of pointed Riemann surfaces.
    Geometry of Riemann surfaces and their moduli spaces, 111-129. Surveys in Differential Geometry 14 (2009).
19. (with R. Salvati Manni) The superstring cosmological constant and the Schottky form in genus 5.
    American Journal of Mathematics 133 (2011) 4, 1007-1027.
18. (with R. Salvati Manni) The vanishing of two-point functions for three-loop superstring scattering amplitudes.
    Communications in Mathematical Physics 294 (2010) 2, 343-352.
17. (with R. Salvati Manni) The loci of abelian varieties with points of high multiplicity on the theta divisor.
    Geometriae Dedicata 139 (2009) 1, 233-247.
16. A special case of the Γ00 conjecture.
    In Liaison, Schottky Problem and Invariant Theory: Remembering Federico Gaeta. Progress in Mathematics 280 (2010), 223-234.
15. Superstring scattering amplitudes in higher genus.
    Communications in Mathematical Physics 287 (2009) 2, 749-767.
14. (with C. Erdenberger, K. Hulek) Some intersection numbers of divisors on toroidal compactifications of Ag.
    Journal of Algebraic Geometry 19 (2010), 99-132.
13. (with I. Krichever) Integrable discrete Schrodinger equations and a characterization of Prym varieties by a pair of quadrisecants.
    Duke Mathematical Journal 152 (2010), 317-371.
12. (with R. Salvati Manni) Singularities of the theta divisor at points of order two.
    International Mathematics Research Notices (2007), paper rnm45.
11. Geometry of Ag and its compactifications.
    Algebraic Geometry: Seattle 2005, Proceedings of Symposia in Pure Mathematics 80, 193-234.
10. (with R. Salvati Manni) Jacobians with a vanishing theta-null in genus 4.
    Israel Journal of Mathematics 164 (2008) 1, 303-315.
9. (with D. Lehavi) Some intersections in the Poincaré bundle, and the universal theta divisor on the moduli space of (semi)abelian varieties.
    International Mathematics Research Notices (2008), paper rnm128.
8. (with C. Erdenberger, K. Hulek) Intersection theory of toroidal compactifications of A4.
    Bulletin of the London Mathematical Society 38 (2006) 3, 396-400.
7. Multiplier ideals in algebraic geometry.
    In Snowbird lectures in Algebraic Geometry (edited by R. Vakil), Contemporary Mathematics 388, AMS 2005, 89-106.
6. (with R. Salvati Manni) Theta functions of arbitrary order and their derivatives.
    Journal fur die reine und angewandte Mathematik (Crelle's Journal), 590 (2006), 31-43.
5. (with R. Salvati Manni) Two generalizations of Jacobi's derivative formula.
    Mathematics Research Letters 12 (2005) 6, 921-932.
4. (with R. Salvati Manni) Gradients of odd theta functions.
    Journal fur die reine und angewandte Mathematik (Crelle's Journal) 573 (2004), 43-59.
3. The degree of the Jacobian locus and the Schottky problem.
2. Cubic equations for the hyperelliptic locus.
    Asian Journal of Mathematics 8 (2004) 1, 161-172 (special issue dedicated to Prof. Yum-Tong Siu on his 60th birthday).
    The PDF incorporates the erratum 9 (2005) 2, 273.
1. An explicit upper bound for Weil-Petersson volumes of the moduli spaces of punctured Riemann surfaces.
    Mathematische Annalen 321 (2001) 1, 1-13.

Here are some notes from my past talks.

6. Printable and on-screen click-through PDF   Moduli of abelian varieties: homology and compactifications (based on papers 8,28,33,39) Berlin, July 2016.
5. Printable and on-screen click-through PDF   Superstring scattering amplitudes and modular forms (based on papers 15,18,19) Hannover, January 2010, and Berlin, July 2010.
4. Printable and on-screen click-through PDF The Schottky Problem (mentioning some results of papers 2,3,10,12,13,16,19) MSRI classical algebraic geometry workshop, January 2009.
3. Printable and on-screen click-through PDF Effective algebraic Schottky problem (based on papers 2 and 3). III Iberoamerican congress on geometry, June 2004.
2. Pages 1, 2, 3, 4, 5, 6, 7, 8, 9. Differential and algebraic equations for theta constants (based on paper 3). AMS meeting, November 2001.
1. Pages 1, 2, 3, 4, 5, 6, 7 Weil-Petersson volumes of moduli of Riemann surfaces (based on paper 1). AMS meeting, March 2000.

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