Brodmann, M (1990). Asymptotic depth and connectedness in projective schemes. Proceedings of the American Mathematical Society, 108(3):573-581.
Let $I \subseteq \mathfrak{m}$ be an ideal of a local noetherian ring (R, m). Consider the exceptional fiber π-1(V(I)) of the blowing-up morphism $\pi: \operatorname{Proj} \bigg(\bigoplus_{n \geq 0}I^n\bigg) \rightarrow \operatorname{Spec}(R)$ and the special fiber π-1(m). We show that the complement set π-1(V(I)) - π-1(m) is highly connected if the asymptotic depth of the higher conormal modules In/In + 1 is large.
Let $I \subseteq \mathfrak{m}$ be an ideal of a local noetherian ring (R, m). Consider the exceptional fiber π-1(V(I)) of the blowing-up morphism $\pi: \operatorname{Proj} \bigg(\bigoplus_{n \geq 0}I^n\bigg) \rightarrow \operatorname{Spec}(R)$ and the special fiber π-1(m). We show that the complement set π-1(V(I)) - π-1(m) is highly connected if the asymptotic depth of the higher conormal modules In/In + 1 is large.
| Item Type: | Journal Article, refereed, original work |
|---|---|
| Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |
| Dewey Decimal Classification: | 510 Mathematics |
| Scopus Subject Areas: | Physical Sciences > General Mathematics
Physical Sciences > Applied Mathematics |
| Uncontrolled Keywords: | connectivity of sheafs, asymptotic depth, topology of the blowing up |
| Language: | English |
| Date: | 1990 |
| Deposited On: | 01 Jun 2010 15:02 |
| Last Modified: | 03 Nov 2023 03:05 |
| Publisher: | American Mathematical Society |
| ISSN: | 0002-9939 |
| Additional Information: | First published in [ Proc. Amer. Math. Soc. 108 (1990), no. 3, 573--581], published by the American Mathematical Society |
| OA Status: | Hybrid |
| Publisher DOI: | https://doi.org/10.2307/2047773 |
| Official URL: | http://www.jstor.org/stable/2047773 |
| Related URLs: | http://www.ams.org/mathscinet-getitem?mr=1031674 http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0695.13012 |
Brodmann, M