Connectedness and Lyubeznik numbers
Commutative Algebra
2017-11-13 v1 Algebraic Geometry
Abstract
We investigate the relationship between connectedness properties of spectra and the Lyubeznik numbers, numerical invariants defined via local cohomology. We prove that for complete equidimensional local rings, the Lyubeznik numbers characterize when connectedness dimension equals one. More generally, these invariants determine a bound on connectedness dimension. Additionally, our methods imply that the Lyubeznik number with indices (1,2) of the local ring at the vertex of the affine cone over a projective variety is independent of the choice of its embedding into projective space.
Cite
@article{arxiv.1711.03655,
title = {Connectedness and Lyubeznik numbers},
author = {Luis Núñez-Betancourt and Sandra Spiroff and Emily Witt},
journal= {arXiv preprint arXiv:1711.03655},
year = {2017}
}
Comments
20 pages, comments welcome