Anatoli Shatsila

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20222026

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10 papers · 1 filter

math.AG2026

Theta-duality and Prym-Torelli for cyclic covers of hyperelliptic curves

Anatoli Shatsila

Let $f : C ~ \to C$ be an étale cyclic cover of odd prime degree $d$ of a hyperelliptic curve of genus $g \geq 2$ . We revisit the theta-duality reconstruction argument for the ge…

math.AG2026

A note on smooth quotients of Prym varieties

Anatoli Shatsila

We study pseudoreflections of geometric origin on Prym varieties of étale double covers. We prove that if the genus of the base curve is $g \geq 4$ then every such pseudoreflection…

math.AG2025

Finiteness and injectivity of Prym maps for cyclic coverings

Paweł Borówka, Juan Carlos Naranjo, Angela Ortega +1

The structure of the Prym map for coverings of degrees $d \geq 3$ is mostly unknown. Only recently, under mild numerical assumptions, a generic injectivity of the Prym maps for étal…

math.AG2025

On the Prym map of degree 4 cyclic covers of hyperelliptic curves

Anatoli Shatsila

In this paper, we study the Prym map associated to degree 4 étale cyclic covers of genus $g$ hyperelliptic curves restricted to the irreducible component $R H_{g} [4]^{h y p}$ …

math.AG2025

Characteristic numbers of algebras

Jakub Jagiełła, Paweł Pielasa, Anatoli Shatsila

We introduce characteristic numbers of a finite commutative unital $C$ -algebra, which are numerical invariants arising from algebraic intersection theory. We characterize…

math.AG2025

On the construction of a counterexample to Strassen's rank additivity conjecture

Viktoriia Borovik, Cosimo Flavi, Paweł Pielasa +2

The rank additivity conjecture, first formulated by Volker Strassen in 1973, states that the rank of the direct sum of two independent tensors is equal to the sum of their individu…

math.AG2025

Pryms of $Z_{3} \times Z_{3}$ coverings of genus 2 curves

Paweł Borówka, Anatoli Shatsila

We study unramified Galois $Z_{3} \times Z_{3}$ coverings of genus 2 curves and the corresponding Prym varieties and Prym maps. In particular, we prove that any such…

math.AG2024

Exact values of generic subrank

Paweł Pielasa, Matouš Šafránek, Anatoli Shatsila

In this article we prove the subrank of a generic tensor in $C^{n, n, n}$ to be $Q (n) = ⌊ 3 n - 2 ⌋$ by providing a lower bound to the known upper bound. Mor…

math.AG2023

Hyperelliptic genus 3 curves with involutions and a Prym map

Paweł Borowka, Anatoli Shatsila

We characterise genus 3 complex smooth hyperelliptic curves that contain two additional involutions as curves that can be build from five points in $P^{1}$ with a distinguis…

math.AG2022

Geometry of elliptic normal curves of degree 6

Anatoli Shatsila

In our work we focus on the geometry of elliptic normal curves of degree 6 embedded in $P^{5}$ . We determine the space of quadric hypersurfaces through an elliptic normal cu…

Theta-duality and Prym-Torelli for cyclic covers of hyperelliptic curves

A note on smooth quotients of Prym varieties

Finiteness and injectivity of Prym maps for cyclic coverings

On the Prym map of degree 4 cyclic covers of hyperelliptic curves

Characteristic numbers of algebras

On the construction of a counterexample to Strassen's rank additivity conjecture

Pryms of Z3​×Z3​ coverings of genus 2 curves

Exact values of generic subrank

Hyperelliptic genus 3 curves with involutions and a Prym map

Geometry of elliptic normal curves of degree 6

Pryms of $Z_{3} \times Z_{3}$ coverings of genus 2 curves