research overview
- Casalaina-Martin performs research in mathematics. He is an algebraic geometer with a broad range of interests. His research focuses on curves, abelian varieties, vector bundles, Hodge theory, and moduli spaces.
- Contact Info
Casalaina-Martin, Sebastian
Positions
- Professor, Mathematics
- Chair, Mathematics
Research Areas
Research
keywords
- Algebraic geometry, curves, abelian varieties, vector bundles, Hodge theory, and moduli spaces
Publications
selected publications
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chapter
- A tour of stable reduction with applications. 65-117. 2013
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The geometry of the ball quotient model of the moduli space of genus four curves.
Contemporary Mathematics.
107-+.
2012
- Singularities of theta divisors in algebraic geometry. Contemporary Mathematics. 25-43. 2008
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conference proceeding
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On the Image of the Second l-adic Bloch Map.
Progress in Mathematics.
15-96.
2019
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On the Image of the Second l-adic Bloch Map.
Progress in Mathematics.
15-96.
2019
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journal article
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DECOMPOSITION OF THE DIAGONAL, INTERMEDIATE JACOBIANS, AND UNIVERSAL CODIMENSION-2 CYCLES IN POSITIVE CHARACTERISTIC.
Asterisque.
1-144.
2025
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The birational geometry of moduli of cubic surfaces and cubic surfaces with a line
2025
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NON-ISOMORPHIC SMOOTH COMPACTIFICATIONS OF THE MODULI SPACE OF CUBIC SURFACES.
Nagoya Mathematical Journal.
315-365.
2024
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The Moduli Space of Cubic Threefolds with a Non-Eckardt Type Involution via Intermediate Jacobians.
International Mathematics Research Notices (IMRN).
16104-16139.
2023
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Cohomology of the Moduli Space of Cubic Threefolds and Its Smooth Models.
Memoirs of the American Mathematical Society.
I-+.
2023
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A functorial approach to regular homomorphisms.
Algebraic Geometry.
87-129.
2023
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The Walker Abel-Jacobi map descends.
Mathematische Zeitschrift.
1799-1817.
2022
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The moduli space of cubic surface pairs via the intermediate Jacobians of Eckardt cubic threefolds.
Journal of the London Mathematical Society.
1-34.
2021
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Complete moduli of cubic threefolds and their intermediate Jacobians.
Proceedings of the London Mathematical Society.
259-316.
2021
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DISTINGUISHED MODELS OF INTERMEDIATE JACOBIANS.
Journal of the Institute of Mathematics of Jussieu.
891-918.
2020
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NORMAL FUNCTIONS FOR ALGEBRAICALLY TRIVIAL CYCLES ARE ALGEBRAIC FOR ARITHMETIC REASONS.
Forum of Mathematics, Sigma.
2019
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Derived equivalent threefolds, algebraic representatives, and the coniveau filtration.
Mathematical Proceedings of the Cambridge Philosophical Society.
123-131.
2019
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Parameter Spaces for Algebraic Equivalence.
International Mathematics Research Notices (IMRN).
1863-1893.
2019
- An introduction to moduli stacks, with a view towards Higgs bundles on algebraic curves 2018
- 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.. Proceedings of the American Mathematical Society. 2018
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GENERIC VANISHING AND MINIMAL COHOMOLOGY CLASSES ON ABELIAN FIVEFOLDS.
Journal of Algebraic Geometry.
553-581.
2018
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On descending cohomology geometrically.
Compositio Mathematica.
1446-1478.
2017
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The singularities and birational geometry of the compactified universal Jacobian.
Algebraic Geometry.
353-393.
2017
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Extending the Prym map to toroidal compactifications of the moduli space of abelian varieties (with an appendix by Mathieu Dutour Sikiric).
Journal of the European Mathematical Society (Print).
659-723.
2017
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The local structure of compactified Jacobians.
Proceedings of the London Mathematical Society.
510-542.
2015
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LOG CANONICAL MODELS AND VARIATION OF GIT FOR GENUS 4 CANONICAL CURVES.
Journal of Algebraic Geometry.
727-764.
2014
- SIMULTANEOUS SEMI-STABLE REDUCTION FOR CURVES WITH ADE SINGULARITIES. Transactions of the American Mathematical Society. 2271-2295. 2013
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The geometry and combinatorics of cographic toric face rings.
Algebra & Number Theory.
1781-1815.
2013
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A RIEMANN SINGULARITY THEOREM FOR INTEGRAL CURVES.
American Journal of Mathematics.
1143-1165.
2012
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Singularities of Brill-Noether loci for vector bundles on a curve.
Mathematische Nachrichten.
1846-1871.
2011
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The moduli space of cubic threefolds via degenerations of the intermediate Jacobian.
Journal für die Reine und Angewandte Mathematik.
29-65.
2009
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Singularities of the Prym theta divisor.
Annals of Mathematics.
163-204.
2009
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Some examples of vector bundles in the base locus of the generalized theta divisor.
Comptes Rendus Mathematique.
173-176.
2009
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Cubic threefolds and abelian varieties of dimension five. II.
Mathematische Zeitschrift.
115-125.
2008
- COHOMOLOGICAL SUPPORT LOCI FOR ABEL-PRYM CURVES. Le Matematiche. 205-222. 2008
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Cubic threefolds and Abelian varieties of dimension five.
Journal of Algebraic Geometry.
295-326.
2005
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DECOMPOSITION OF THE DIAGONAL, INTERMEDIATE JACOBIANS, AND UNIVERSAL CODIMENSION-2 CYCLES IN POSITIVE CHARACTERISTIC.
Asterisque.
1-144.
2025
Background
education and training
- M.Phil., Columbia University In the City of New York 2004
- Ph.D., Columbia University In the City of New York 2004
- M.A., Columbia University In the City of New York 2000
- B.S., Brown University 1998