Lefschetz duality for local cohomology
Abstract
Since the 1974 paper by Peskine and Szpiro, liaison theory via complete intersections, and more generally via Gorenstein varieties, has become a standard tool kit in commutative algebra and algebraic geometry, allowing to compare algebraic features of linked varieties. In this paper we develop a liaison theory via quasi-Gorenstein varieties, a much broader class than Gorenstein varieties: it is not misleading to think that quasi-Gorenstein rings are to Gorenstein rings as manifolds are to spheres. As applications, we derive a connectedness property of quasi-Gorenstein subspace arrangements generalizing previous results by Benedetti and the second author, and we deduce the classical topological Lefschetz duality via the Stanley-Reisner correspondence.
Keywords
Cite
@article{arxiv.2208.11504,
title = {Lefschetz duality for local cohomology},
author = {Matteo Varbaro and Hongmiao Yu},
journal= {arXiv preprint arXiv:2208.11504},
year = {2024}
}
Comments
16 pages. The section distribution has been revised in this new version, and we have also corrected some typos and errors