Korff $F$-signatures of Hirzebruch surfaces

TL;DR

This paper computes the $F$-signatures of Hirzebruch surfaces, extending previous work on simpler varieties and providing explicit formulas for these invariants.

Contribution

The paper provides explicit calculations of the $F$-signatures for all Hirzebruch surfaces, expanding the class of varieties with known $F$-signatures.

Findings

Explicit formulas for $F$-signatures of Hirzebruch surfaces

Extension of $F$-signature computations to new classes of surfaces

Enhancement of understanding of $F$-signatures in algebraic geometry

Abstract

M. Von Korff introduced the $F$-signature of a normal projective variety, and computed the $F$-signature of the product of two projective lines $\mathbb{P}^1\times \mathbb{P}^1$. In this paper, we compute $F$-signatures of Hirzebruch surfaces.