2010
DOI: 10.1016/j.jalgebra.2010.07.023
|View full text |Cite
|
Sign up to set email alerts
|

On the cohomology of a simple normal crossings divisor

Abstract: We establish a formula which decomposes the cohomologies of various sheaves on a simple normal crossings divisor (SNC) D in terms of the simplicial cohomologies of the dual complex (D)with coefficients in a presheaf of vector spaces. This presheaf consists precisely of the corresponding cohomology data on the components of D and on their intersections. We use this formula to give a Hodge decomposition for SNC divisors and investigate the toric setting. We also conjecture the existence of such a formula for eff… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
1
1

Citation Types

0
2
0

Year Published

2013
2013
2020
2020

Publication Types

Select...
2
1

Relationship

1
2

Authors

Journals

citations
Cited by 3 publications
(2 citation statements)
references
References 23 publications
0
2
0
Order By: Relevance
“…Note added: after this work was completed and posted as a preprint, we became aware of [16], which arrives at results that have some overlap with ours, in the special case that the CW complex is in fact a simplicial complex.…”
Section: Introductionmentioning
confidence: 92%
“…Note added: after this work was completed and posted as a preprint, we became aware of [16], which arrives at results that have some overlap with ours, in the special case that the CW complex is in fact a simplicial complex.…”
Section: Introductionmentioning
confidence: 92%
“…. Furthermore, by Remark 5.5 in [4], H i (O D ) depends entirely on the simplicial complex ∆(D), which is constructed using only the incidence information among the D i 0 ...ip .…”
Section: A Technical Lemmamentioning
confidence: 99%