arXiv subjects

Constantin Podelski

Publications and source records attributed to Constantin Podelski.

4 recordsLinked to original sources

arXiv2025

Singularities of theta divisors and the Tannakian Schottky problem

With the Tannakian formalism, one can attach to any principally polarized abelian variety a reductive group, along with a representation. We obtain a completely new characterization of Jacobians relying on this Tannakian data and certain characteristic classes for singular varieties. As a corollary, we show that the Tannakian Schottky conjecture holds in dimension up to $5$. More generally, we show that the Tannakian Schottky conjecture holds on the bielliptic Prym locus in all dimensions. This provides the first non-trivial cases of this conjecture.

math.AG↗

arXiv2024

The Gauss map for bielliptic Prym varieties

We completely describe the degree of the Gauss map of the theta divisor of bielliptic Prym varieties. We characterize bielliptic Prym varieties whose Gauss degree is the same as Jacobians. We also construct bielliptic Prym varieties with a very low Gauss degree. In dimension $5$, we obtain a complete description of the Gauss degree on the Andreotti-Mayer locus.

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arXiv2024

The Gauss Map on Theta Divisors with Transversal $\mathrm{A}_1$ Singularities

We use Lagrangian specialization to compute the degree of the Gauss map on Theta divisors with transversal $\mathrm{A}_1$ singularities. This computes the Gauss degree for a general abelian variety in the loci $\mathcal{A}^δ_{t,g-t}$ that form some of the irreducible components of the Andreotti-Mayer loci. We also prove that the first coefficient of the Lagrangian specialization is the Samuel multiplicity of the singular locus.

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arXiv2023

The boundary of the bielliptic Prym locus

We study the conormal geometry theta divisors of certain singular bielliptic curves. We apply these results to the boundary components $\mathscr{S}_\underline{d}$ of the bielliptic Prym locus. We obtain results on the Gauss map, compute the Chern-Mather class and the characteristic cycle of the intersection complex of the corresponding Prym theta divisor.

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