Canonical cohomology as an exterior module

2010/10/25 by Robert Lazarsfeld, Lazarsfeld, Robert, Mihnea Popa +3
Mathematics · #14C30 #14F05 #14F17 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14C30 #msc:14F05 #msc:14F17

paper · pdf · doi:10.48550/arxiv.1010.5026

10 pages; restricted the hypothesis to smooth projective varieties; to appear in the Eckart Viehweg memorial issue of Pure and Applied Math. Quarterly

arxiv created 2011/05/05 · arxiv updated 2011/05/06

Abstract

We show that the total cohomology of the canonical bundle of a smooth projective variety, seen as a module over an exterior algebra, splits into a natural direct sum of submodules which are generated in degree zero and have a linear free resolution. This improves a previous result of the first two authors.

Related

• Cohomology over complete intersections via exterior algebras
• Hyperplane Arrangement Cohomology and Monomials in the Exterior Algebra
• Canonical modules of complexes
• Generalized local duality, canonical modules, and prescribed bound on projective dimension
• Hochschild (co)homology of exterior algebras