arXiv subjects

Francesca Leonardi

Publications and source records attributed to Francesca Leonardi.

2 recordsLinked to original sources

arXiv2026

Logarithmic Hochschild (co)homology of logarithmic orbifolds

Recently, the authors of this paper introduced logarithmic Hochschild (co)homology of logarithmic spaces in a geometric way using formality of derived intersections. In this paper, the authors extend the decomposition theorem for the logarithmic Hochschild (co)homology of firm orbifolds to general logarithmic orbifolds and consider two applications of the decomposition theorem. First, we consider two versions of a symmetric product and compute the logarithmic Hochschild homology of them. Second, we show that logarithmic Hochschild homology is invariant under root stack operations.

math.AG↗

arXiv2024

Logarithmic Hochschild co/homology via formality of derived intersections

We define log Hochschild co/homology for log schemes that behaves well for simple normal crossing pairs $(X,D)$ or toroidal singularities. We prove a Hochschild-Kostant-Rosenberg isomorphism for log smooth schemes, as well as an equivariant version for log orbifolds. We define cyclic homology and compute it in simple cases. We show that log Hochschild co/homology is invariant under log alterations. Our main technical result in log geometry shows the tropicalization (Artin fan) of a product of log schemes $X \times Y$ is usually the product of the tropicalizations of $X$ and $Y$. This and the machinery of \emph{formality} of derived intersections facilitate a geometric approach to log Hochschild.

math.AG↗