Sebastian Casalaina

Summary

I am an algebraic geometer with a broad range of interests. My research focuses on curves, abelian varieties, cubic threefolds, vector bundles and moduli spaces. 

My papers and preprints are available below, as well as on the arXiv.

Preprints and papers

  1. Derived equivalent threefolds, algebraic representatives, and the coniveau filtration, with Jeff Achter and Charles Vial, preprint.

  2. Derived equivalent varieties have isogenous Picard varieties, with Jeff Achter, Katrina Honigs and Charles Vial; appendix to Derived equivalence, Albanese varieties, and the zeta functions of 3-dimensional varieties, by Katrina Honigs, to appear in Proc. Amer. Math. Soc.

  3. Distinguished models of intermediate Jacobians, with Jeff Achter and Charles Vial, preprint.

  4. Parameter spaces for algebraic equivalence, with Jeff Achter and Charles Vial, to appear in IMRN.

  5. Generic vanishing and minimal cohomology classes on abelian fivefolds, with Mihnea Popa and Stefan Schreieder, to appear in J. Algebraic Geom.

  6. Complete moduli of cubic threefolds and their intermediate Jacobians, with Samuel Grushevsky, Klaus Hulek and Radu Laza, preprint.

  7. An introduction to moduli stacks, with a view towards Higgs bundles on algebraic curves, with Jonathan Wise, to appear in the NUS IMS Lecture Note Series on The Geometry, Topology and Physics of Moduli Spaces of Higgs Bundles.

  8. On descending cohomology geometrically, with Jeff Achter and Charles Vial, Compositio Math. 153 (2017), no. 7, 1446--1478.

  9. The singularities and birational geometry of the universal compactified Jacobian, with Jesse Kass and Filippo Viviani, Algebraic Geometry 4 (2017), no. 3, 353--393.

  10. Extending the Prym map to toroidal compactifications of the moduli space of abelian varieties, with Samuel Grushevsky, Klaus Hulek and Radu Laza, (with an appendix by Mathieu Dutour Sikiric), J. Eur. Math. Soc. (JEMS) 19 (2017), no. 3, 659--723.

  11. A tour of stable reduction with applications, A celebration of algebraic geometry, 65--117, Clay Math. Proc., 18, Amer. Math. Soc., Providence, RI, 2013.

  12. Log canonical models and variation of GIT for genus four canonical curves, with David Jensen and Radu Laza, J. Algebraic Geom. 23 (2014), no. 4, 727--764.

  13. The geometry of the ball quotient model of the moduli space of genus four curves, with David Jensen and Radu Laza, Compact moduli spaces and vector bundles, 107--136, Contemp. Math., Amer. Math. Soc., Providence, RI, 2012.

  14. The local structure of compactified Jacobians, with Jesse Kass and Filippo Viviani, Proc. Lond. Math. Soc. 110 (2015), no. 2, 510--542.

  15. The geometry and combinatorics of cographic toric face rings, with Jesse Kass and Filippo Viviani, Algebra and Number Theory 7 (2013), no. 8, 1781--1815.

  16. Simultaneous semi-stable reduction for curves with ADE singularities, with Radu Laza, Trans. Amer. Math. Soc. 365 (2013), no. 5, 2271--2295.

  17. A Riemann singularity theorem for integral curves, with Jesse Kass, Amer. J. Math., 134 (2012), no. 5, 1143--1165.

  18. Cohomological support loci for Abel-Prym curves, with Marti Lahoz and Filippo Viviani, Matematiche (Catania), Vol. LXIII (2008) -- Fasc. I, 205--222.

  19. The moduli space of cubic threefolds via degenerations of the intermediate Jacobian, with Radu Laza, J. reine angew. Math. (Crelle) 633 (2009), 29--65.

  20. Singularities of theta divisors in algebraic geometry,  Curves and abelian varieties, 25--43, Contemp. Math., 465, Amer. Math. Soc., Providence, RI, 2008.

  21. Singularities of Brill-Noether loci for vector bundles on curves, with Montserrat Teixidor i Bigas, Math. Nach. 284 (2011), no. 14-15, 1846--1871.

  22. Some examples of vector bundles in the base locus of the generalized theta divisor, with Tawanda Gwena and Montserrat Teixidor i Bigas, C. R. Math. Acad. Sci. Paris 347 (2009), no. 3-4, 173--176.

  23. Cubic threefolds and abelian varieties of dimension five. II,  Math. Z. 260 (2008), no. 1, 115--125.

  24. Singularities of the Prym theta divisor, Ann. of Math. 170 (2009), no. 1, 163--204.

  25. Cubic threefolds and abelian varieties of dimension five, with Robert Friedman,  J. Algebraic Geom. 14 (2005), no. 2, 295--326.

Preprints and papers on other topics

In addition to my research in algebraic geometry, I have recently begun some collaborative work on a topic in computer science. You can find out more about this here.