Andrea Gallese

collaborators

5 papers

math.NT2026

Monodromy groups and exceptional Hodge classes, I: Fermat Jacobians

Andrea Gallese, Heidi Goodson, Davide Lombardo

Denote by $J_{m}$ the Jacobian variety of the hyperelliptic curve defined by the affine equation $y^{2} = x^{m} + 1$ over $Q$ , where $m \geq 3$ is a fixed positive integer. We compu…

math.NT2026

Finding the complement of an elliptic curve inside a Jacobian

Andrea Gallese, Davide Lombardo, Francesco Naccarato +1

This note gives a simple algorithm for the following effectivity problem: given a genus $2$ curve $X$ together with a nonconstant map $I ¨ : X \to E$ to an elliptic curve, determine an…

math.NT2025

Connected monodromy fields of Jacobians with complex multiplication

Andrea Gallese, Davide Lombardo

We describe an algorithm to compute the minimal field of definition of the Tate classes on powers of a Jacobian $J$ with potential complex multiplication. This field arises as a na…

math.NT2025

Monodromy groups and exceptional Hodge classes, II: Sato-Tate groups

Andrea Gallese, Heidi Goodson, Davide Lombardo

Denote by $J_{m}$ the Jacobian variety of the hyperelliptic curve defined by the affine equation $y^{2} = x^{m} + 1$ over $Q$ , where $m \geq 3$ is a fixed positive integer. In this…

math.AG2025

How to split two-dimensional Jacobians: a geometric construction

Andrea Gallese

Let $I ¨ : Y \to X$ be a branched cover of algebraic curves. Assume that there exists a curve $W$ such that $\operatorname{Jac} Y \sim \operatorname{Jac} X \times \operatorname{…