Logarithmic Hochschild (co)homology of logarithmic orbifolds

TL;DR

This paper extends the decomposition theorem for logarithmic Hochschild (co)homology to general logarithmic orbifolds, computes it for symmetric products, and proves its invariance under root stack operations.

Contribution

It generalizes the decomposition theorem for logarithmic Hochschild (co)homology and explores its applications to symmetric products and root stacks.

Findings

Decomposition theorem extended to all logarithmic orbifolds.

Logarithmic Hochschild homology computed for symmetric products.

Invariance under root stack operations established.

Abstract

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.