arXiv subjects

Alexia Corradini

Publications and source records attributed to Alexia Corradini.

3 recordsLinked to original sources

arXiv2026

Algebraically trivial tropical cycles are smash-nilpotent

We prove that if $Z$ is a tropical cycle in a tropical variety $Y$ which is algebraically trivial, then for $k\gg1$ sufficiently large, $k!\cdot Z^k\subset Y^k$ is rationally trivial. The proof involves explicitly constructing a rational equivalence $k!\cdot(p-q)^k\sim0$ in the product $C^k$, where $p$ and $q$ are any points on $C$. We use this to formulate a tropical version of Voevodsky's conjecture, provide explicit examples, and comment on potential applications to symplectic geometry.

math.AG↗

arXiv2025

Algebraic Lagrangian cobordisms, flux and the Lagrangian Ceresa cycle

We introduce an equivalence relation for Lagrangians in a symplectic manifold known as \textit{algebraic Lagrangian cobordism}, which is meant to mirror algebraic equivalence of cycles. From this we prove a symplectic, mirror-symmetric analogue of the statement \enquote{the Ceresa cycle is non-torsion in the Griffiths group of the Jacobian of a generic genus $3$ curve}. Namely, we show that for a family of tropical curves, the \textit{Lagrangian Ceresa cycle}, which is the Lagrangian lift of their tropical Ceresa cycle to the corresponding Lagrangian torus fibration, is non-torsion in its oriented algebraic Lagrangian cobordism group. We proceed by developing the notions of tropical (resp. symplectic) flux, which are morphisms from the tropical Griffiths (resp. algebraic Lagrangian cobordism) groups.

math.SG↗

arXiv2022

Equivariant localisation in the theory of $Z$-stability for Kähler manifolds

We apply equivariant localisation to the theory of $Z$-stability and $Z$-critical metrics on a Kähler manifold $(X,α)$, where $α$ is a Kähler class. We show that the invariants used to determine $Z$-stability of the manifold, which are integrals over test configurations, can be written as a product of equivariant classes, hence equivariant localisation can be applied. We also study the existence of $Z$-critical Kähler metrics in $α$, whose existence is conjectured to be equivalent to $Z$-stability of $(X,α)$. In particular, we study a class of invariants that give an obstruction to the existence of such metrics. Then we show that these invariants can also be written as a product of equivariant classes. From this we give a new, more direct proof of an existing result: the former invariants determining $Z$-stability on a test configuration are equal to the latter invariants related to the existence of $Z$-critical metrics on the central fibre of the test configuration. This provides a new approach from which to derive the $Z$-critical equation.

math.DG↗