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, moduli spaces, and Hodge theory. 

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

Preprints and papers

  1. The birational geometry of moduli of cubic surfaces and cubic surfaces with a lines, with Samuel Grushevsky, and Klaus Hulek, preprint.

  2. Putting the p back in Prym, with Jeff Achter, preprint.

  3. Images of abelian schemes, with Jeff Achter, preprint.

  4. The moduli space of cubic threefolds with a non-Eckardt type involution via intermediate Jacobians, with Lisa Marquand and Zheng Zhang, Int. Math. Res. Not. IMRN (2023), no. 18, 16104--16139.

  5. A complete answer to Albanese base change for incomplete varieties, with Jeff Achter and Charles Vial, preprint.

  6. Non-isomorphic smooth compactifications of the moduli space of cubic surfaces, with Samuel Grushevsky, Klaus Hulek, and Radu Laza, to appear in Nagoya Math. J.

  7. The Walker Abel-Jacobi map descends, with Jeff Achter and Charles Vial, Math. Z. 300 (2022), no. 2, 1799--1817.

  8. The algebraic Abel-Prym map; appendix to Kirchhoff's theorem for Prym varieties, by Yoav Len and Dmitry Zakharov, Forum of Mathematics, Sigma (2022), Vol. 10:e11 1-54.

  9. Decomposition of the diagonal, intermediate Jacobians, and universal codimension-2 cycles in positive characteristic, with Jeff Achter and Charles Vial, to appear in Asterisque.

  10. On the image of the second l-adic Bloch map, with Jeff Achter and Charles Vial, Rationality of Varieties, 15--73, Progr. Math., 342, Birkhauser/Springer, Cham, (2021).

  11. The moduli space of cubic surface pairs via the intermediate Jacobians of Eckardt cubic threefolds, with Zheng Zhang, J. Lond. Math. Soc. 104 (2021), no. 1, 1--34.

  12. A functorial approach to regular homomorphisms, with Jeff Achter and Charles Vial, Algebr. Geom. 10 (2023), no. 1, 87--129.

  13. Cohomology of the moduli space of cubic threefolds and its smooth models, with Samuel Grushevsky, Klaus Hulek, and Radu Laza, Mem. Amer. Math. Soc. 282 (2023), no. 1395, v+100 pp.

  14. Normal functions for algebraically trivial cycles are algebraic for arithmetic reasons, with Jeff Achter and Charles Vial, Forum of Mathematics, Sigma 7 (2019), Paper No. e36, 22 pp.

  15. Derived equivalent threefolds, algebraic representatives, and the coniveau filtration, with Jeff Achter and Charles Vial, Math. Proc. Cambridge Philos. Soc. 167 (2019), no. 1, 123--131.

  16. 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, Proc. Amer. Math. Soc. 146 (2018), no.3, 1005--10013.

  17. Distinguished models of intermediate Jacobians, with Jeff Achter and Charles Vial, J. Inst. Math. Jussieu 19 (2020), no. 3, 891--918.

  18. Parameter spaces for algebraic equivalence, with Jeff Achter and Charles Vial, Int. Math. Res. Not. IMRN 2019, no. 6, 1863--1893.

  19. Generic vanishing and minimal cohomology classes on abelian fivefolds, with Mihnea Popa and Stefan Schreieder, J. Algebraic Geom. 27 (2018), 553--581.

  20. Complete moduli of cubic threefolds and their intermediate Jacobians, with Samuel Grushevsky, Klaus Hulek, and Radu Laza, Proc. Lond. Math. Soc. 122 (3), (2021), 259--316.

  21. An introduction to moduli stacks, with a view towards Higgs bundles on algebraic curves, with Jonathan Wise, The geometry, topology and physics of moduli spaces of Higgs bundles, 199--399, Lect. Notes Ser. Inst. Math. Sci. Natl. Univ. Singap., 36, World Sci. Publ., Hackensack, NJ, 2018.

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

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

  24. 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.

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

  26. 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.

  27. 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., 564, Amer. Math. Soc., Providence, RI, 2012.

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

  29. 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.

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

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

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

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

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

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

  36. 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.

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

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

  39. 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.


Department of Mathematics
University of Colorado