2011/03/09 by Samuel Grushevsky, Klaus Hulek, Grushevsky, Samuel +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #math.AG
paper · pdf · doi:10.48550/arxiv.1103.1858
openalex publication_date 2011/03/09 · arxiv created 2011/04/21 · arxiv updated 2011/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We obtain, by a direct computation, explicit descriptions of all principally polarized semi-abelic varieties of torus rank up to 3. We describe the geometry of their symmetric theta divisors and obtain explicit formulas for the involution and its fixed points. These results allow us to give a new proof of the statements about the dimensions, for small genus, of the loci of ppav with theta divisor containing two-torsion points of multiplicity three. We also prove a result about the closure of this set. Our computations used in our work arXiv:1103.1857 to compute the class of the closure of the locus of intermediate jacobians of cubic threefolds in the Chow ring of the perfect cone compactification of the moduli space of principally polarized abelian fivefolds.