Research

Interests:

Algebraic Geometry: moduli spaces of curves and Jacobians, modular compactifications and enumerative questions

Tropical Geometry: Moduli spaces of tropical curves and tropical Abelian varieties, linear series on tropical curves.

 


Papers:

- Combinatorial aspects of nodal curves (with S. Busonero and L. Stoppino). Le Matematiche 61 (2006), no. 1, 109-141.

- Compactified Picard stacks over Mg. Mathematische Zeitschricht 263 (2009), no. 4, 939-957.

- Compactified Picard stacks over the moduli stack of stable curves with marked points. Advances in Mathematics 226 (2011) No. 1, 727-763.

- On the complexity group of stable curves (with Simone Busonero and Lidia Stoppino).  Advances in Geometry 11 (2011), no. 2, 241-272.

- On the Tropical Torelli map (with Silvia Brannetti and Filippo Viviani).  Advances in Mathematics 226 (2011) No. 3, 2546-2586.

- Fine compactified Jacobians (with Filippo Viviani). Mathematische Nachrichten 285 (2012) No. 8-9, 997–1031.

- Comparing Perfect and Voronoi decompositions: the matroidal locus (with Filippo Viviani).  Mathematische Annalen 354 (2012) No. 4,  1521-1554.

- On GIT quotients of Hilbert and Chow schemes of curves (with Gilberto Bini and Filippo Viviani). Electronic Research Announcements in Mathematical Sciences 19 (2012), 33-40.

- Tropical Teichmüller and Siegel Spaces (with Melody Chan and Filippo Viviani). Contemporary Mathematics (Proceedings of the CIEM Workshop on tropical geometry) 589 (2013), 45-85.

- Picard group of the compactified universal Picard stack (with Filippo Viviani). Documenta Mathematica 19 (2014), 457-507.

- Algebraic and combinatorial rank of divisors on finite graphs (with Lucia Caporaso, Yoav Len, Margarida Melo). To appear in Journal des Mathematiques Pures et Appliquees. Preprint arXiv:1401.5730.

Fine compactified Jacobians of reduced curves (with Antonio Rapagnetta and Filippo Viviani). To appear in Transactions of Mathematics. Preprint arXiv:1406.2299.

Preprints:

- Fourier-Mukai and Autoduality for Compactified Jacobians. I (with Antonio Rapagnetta and Filippo Viviani and an Appendix by A. C. López Martín). Preprint arXiv:1207.7233.


- Fourier-Mukai and Autoduality for Compactified Jacobians. II (with Antonio Rapagnetta and Filippo Viviani), 35 p. Submitted. Preprint arXiv:1308.0564.

 

 

Book:

- GIT for polarized curves (with Gilberto Bini, Fabio Felice and Filippo Viviani).   Lecture Notes in Mathematics 2122. Springer, 2014.