On Yuzvinsky’s lattice sheaf cohomology for hyperplane arrangements

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Autoren

  • Paul Mücksch

Externe Organisationen

  • Kyushu University
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Details

OriginalspracheEnglisch
Seiten (von - bis)1513–1531
Seitenumfang19
FachzeitschriftMathematische Annalen
Jahrgang387
Ausgabenummer3-4
Frühes Online-Datum31 Okt. 2022
PublikationsstatusVeröffentlicht - Dez. 2023
Extern publiziertJa

Abstract

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.

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On Yuzvinsky’s lattice sheaf cohomology for hyperplane arrangements. / Mücksch, Paul.
in: Mathematische Annalen, Jahrgang 387, Nr. 3-4, 12.2023, S. 1513–1531.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Mücksch P. On Yuzvinsky’s lattice sheaf cohomology for hyperplane arrangements. Mathematische Annalen. 2023 Dez;387(3-4):1513–1531. Epub 2022 Okt 31. doi: 10.1007/s00208-022-02499-1
Mücksch, Paul. / On Yuzvinsky’s lattice sheaf cohomology for hyperplane arrangements. in: Mathematische Annalen. 2023 ; Jahrgang 387, Nr. 3-4. S. 1513–1531.
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