Local cohomology and the connectedness dimension in algebraic varieties
type: Item
instance of: scholarly article
title: Local cohomology and the connectedness dimension in algebraic varieties
zbMATH Open document ID: 0578.14019
DOI: 10.1007/BF02621928
author: Josef Rung
author: M. P. Brodmann
published in: Commentarii Mathematici Helvetici
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/140064
review text: Let Z be a closed set of a noetherian scheme X. We define the connectedness dimension c(Z) of Z as the minimal value of dim(W), where W runs through all closed subsets of Z such that Z-W is disconnected. Using standard tools from local cohomology (Mayer-Vietoris sequences and vanishing theorems) we give bounds for c(Z) and connectedness criteria for Z. This gives a unified approach to study connectivity of intersections and of fibers. In particular one gets easy proofs for the connectedness theorem of Fulten-Hansen, and for (sharpened versions) of Zariski's connectedness theorem for projective morphisms and also for the connectedness statements of Bertini's theorems.
Mathematics Subject Classification ID: 14F45
Mathematics Subject Classification ID: 14B15
Mathematics Subject Classification ID: 54F45
Mathematics Subject Classification ID: 14C17
zbMATH DE Number: 3924971
zbMATH Keywords: Bertini theorems
zbMATH Keywords: connectedness theorems
zbMATH Keywords: noetherian scheme
zbMATH Keywords: connectedness dimension
zbMATH Keywords: local cohomology
zbMATH Keywords: intersections
zbMATH Keywords: fibers
MaRDI profile type: Publication
OpenAlex ID: W2086484895
description: scientific article; zbMATH DE number 3924971