[en] We compute the Hochschild–Kostant–Rosenberg decomposition of the Hochschild cohomology of Fano 3-folds. This is the first step in understanding the non-trivial Gerstenhaber algebra structure of this invariant, and yields some initial insights in the classification of Poisson structures on Fano 3-folds of higher Picard rank.
Disciplines :
Mathematics
Author, co-author :
BELMANS, Pieter ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH)
Fatighenti, Enrico; Dipartimento di Matematica, Università di Bologna, Bologna, Italy
Tanturri, Fabio; Dipartimento di Matematica, Università di Genova, Genova, Italy
External co-authors :
yes
Language :
English
Title :
Polyvector fields for Fano 3-folds
Publication date :
May 2023
Journal title :
Mathematische Zeitschrift
ISSN :
0025-5874
eISSN :
1432-1823
Publisher :
Springer Science and Business Media Deutschland GmbH
Open access funding provided by Università degli Studi di Genova within the CRUI-CARE Agreement.We would like to thank Marcello Bernardara, Alexander Kasprzyk, Brent Pym and Helge Ruddat for interesting conversations. We want to thank Burt Totaro for pointing out the subtletly explained in Remark 3.6. We want to thank the referee for a careful reading and interesting comments that improved the paper. And most of all we want to thank Alexander Kuznetsov for many conversations over the years about Fano 3-folds, and comments on an earlier version of this paper. The first author was partially supported by the FWO (Research Foundation–Flanders). The second and third author are members of INdAM-GNSAGA.We would like to thank Marcello Bernardara, Alexander Kasprzyk, Brent Pym and Helge Ruddat for interesting conversations. We want to thank Burt Totaro for pointing out the subtletly explained in Remark . We want to thank the referee for a careful reading and interesting comments that improved the paper. And most of all we want to thank Alexander Kuznetsov for many conversations over the years about Fano 3-folds, and comments on an earlier version of this paper. The first author was partially supported by the FWO (Research Foundation–Flanders). The second and third author are members of INdAM-GNSAGA.
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