On Lyubeznik type invariants

TL;DR

This paper explores Lyubeznik type invariants for affine varieties, providing topological interpretations and examining their properties in small dimensions and for projective varieties.

Contribution

It introduces and analyzes two sets of invariants associated with affine varieties using local and de Rham cohomology spectral sequences, with new topological insights.

Findings

Topological interpretations of the invariants

Analysis of invariants in small dimensions

Investigation of invariants for projective varieties

Abstract

We discuss for an affine variety $Y$ embedded in affine space $X$ two sets of integers attached to $Y\subseteq X$ via local and de Rham cohomology spectral sequences. We give topological interpretations, study them in small dimension, and investigate to what extent one can attach them to projective varieties.