Details
| Original language | English |
|---|---|
| Pages (from-to) | 1513–1531 |
| Number of pages | 19 |
| Journal | Mathematische Annalen |
| Volume | 387 |
| Issue number | 3-4 |
| Early online date | 31 Oct 2022 |
| Publication status | Published - Dec 2023 |
| Externally published | Yes |
Abstract
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In: Mathematische Annalen, Vol. 387, No. 3-4, 12.2023, p. 1513–1531.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On Yuzvinsky’s lattice sheaf cohomology for hyperplane arrangements
AU - Mücksch, Paul
N1 - Publisher Copyright: © 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2023/12
Y1 - 2023/12
N2 - We establish the relationship between the cohomology of a certain sheaf on the intersection lattice of a hyperplane arrangement introduced by Yuzvinsky and the cohomology of the coherent sheaf on punctured affine space, respectively projective space associated to the module of logarithmic vector fields along the arrangement. Our main result gives a Künneth formula connecting the cohomology theories, answering a question by Yoshinaga. This, in turn, provides a characterization of the projective dimension of the module of logarithmic vector fields and yields a new proof of Yuzvinsky’s freeness criterion. Furthermore, our approach affords a new formulation of Terao’s freeness conjecture and a more general problem.
AB - We establish the relationship between the cohomology of a certain sheaf on the intersection lattice of a hyperplane arrangement introduced by Yuzvinsky and the cohomology of the coherent sheaf on punctured affine space, respectively projective space associated to the module of logarithmic vector fields along the arrangement. Our main result gives a Künneth formula connecting the cohomology theories, answering a question by Yoshinaga. This, in turn, provides a characterization of the projective dimension of the module of logarithmic vector fields and yields a new proof of Yuzvinsky’s freeness criterion. Furthermore, our approach affords a new formulation of Terao’s freeness conjecture and a more general problem.
UR - http://www.scopus.com/inward/record.url?scp=85140974461&partnerID=8YFLogxK
U2 - 10.1007/s00208-022-02499-1
DO - 10.1007/s00208-022-02499-1
M3 - Article
VL - 387
SP - 1513
EP - 1531
JO - Mathematische Annalen
JF - Mathematische Annalen
SN - 0025-5831
IS - 3-4
ER -