Log canonical threshold, Segre classes, and polygamma functions

TL;DR

This paper links Segre classes of monomial schemes with log canonical thresholds and derives identities involving polygamma functions, revealing new connections between algebraic geometry and special functions.

Contribution

It provides a novel expression of Segre classes in terms of log canonical thresholds and establishes identities with classical polygamma functions.

Findings

Segre class of monomial schemes expressed via log canonical thresholds

Identities involving classical polygamma functions derived

Explicit relations connecting algebraic geometry and special functions

Abstract

We express the Segre class of a monomial scheme in projective space in terms of log canonical thresholds of associated ideals. Explicit instances of the relation amount to identities involving the classical polygamma functions.