Lyubeznik numbers of irreducible projective varieties depend on the embedding

TL;DR

This paper demonstrates that Lyubeznik numbers of affine cones over irreducible projective varieties can vary depending on the embedding, challenging previous assumptions of their invariance.

Contribution

It constructs examples of irreducible projective varieties with Lyubeznik numbers that depend on the embedding, utilizing perverse sheaves and recent theoretical developments.

Findings

Lyubeznik numbers depend on the embedding of the variety.

Construction of irreducible varieties with embedding-dependent Lyubeznik numbers.

Application of perverse sheaves to interpret Lyubeznik numbers.

Abstract

We construct irreducible complex projective varieties such that the Lyubeznik numbers of their affine cones depend on the choices of projective embeddings. The main ingredient is the recent work of Reichelt-Saito-Walther, where the Lyubeznik numbers are reinterpreted using perverse sheaves and reducible projective varieties with dependent Lyubeznik numbers are constructed.