We use a differential form cohomology theory on transitive digraphs to give a new proof of a theorem of Gerstenhaber and Schack about isomorphism between simplicial cohomology and Hochschild cohomology of a certain algebra associated with the simplicial complex.
Mauricio BustamanteDEPARTMENT OF PURE MATHEMATICS AND MATHEMATICAL SCIENCES, UNIVERSITY OF CAMBRIDGE,UKFrancis Thomas FarrellYAU MATHEMATICAL SCIENCES CENTER,TSINGHUA UNIVERSITY,BEIJING,CHINAYi JiangYAU MATHEMATICAL SCIENCES CENTER,TSINGHUA UNIVERSITY,BEIJING,CHINA
Algebraic Topology and General Topologymathscidoc:2204.44002
Transactions of the American Mathematical Sciences, 373, (10), 7225-7252, 2020.10
We construct a cohomology theory of transitive digraphs and use it to give a new proof of a theorem of Gerstenhaber and Schack about isomorphism between simplicial cohomology and Hochschild cohomology of a certain algebra associated with the simplicial complex.
Ciro CilibertoDipartimento di Matematica, Università di Roma Tor Vergata, Roma, ItalyThomas DedieuInstitut de Mathématiques de Toulouse, Université de Toulouse, FranceConcettina GalatiDipartimento di Matematica e Informatica, Università della Calabria, Arcavacata di Rende (CS), ItalyAndreas Leopold KnutsenDepartment of Mathematics, University of Bergen, Norway
Algebraic Topology and General Topologymathscidoc:2203.44001
We prove that the locus of Prym curves (C,η) of genus g≥5 for which the Prym-canonical system |ωC(η)| is base point free but the Prym-canonical map is not an embedding is irreducible and unirational of dimension 2g+1.