Groebner deformations, connectedness and cohomological dimension

TL;DR

This paper explores the relationship between connectedness properties and (local) cohomological dimension, demonstrating that initial complexes of Cohen-Macaulay ideals are strongly connected, thus linking algebraic and topological properties.

Contribution

It establishes new results connecting connectedness with cohomological dimension and shows that initial complexes of Cohen-Macaulay ideals are strongly connected.

Findings

Connectedness properties relate to (local) cohomological dimension.

Initial complexes of Cohen-Macaulay ideals are strongly connected.

Provides theoretical insights into algebraic and topological structures.

Abstract

This paper is an outcome of the author's master thesis written under the supervision of Aldo Conca. We prove some results relating connectedness properties with (local) cohomological dimension. As an interesting corollary we have that every initial complex of a Cohen-Macaulay ideal is strongly connected.