Hodge cohomology on blow-ups along subvarieties

2019/07/31 by Sheng Rao, Song Yang, Rao, Sheng +5 · 2 citations
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.1907.13281

Abstract

We establish a blow-up formula for Hodge cohomology of locally free sheaves on smooth proper varieties over an algebraically closed field of positive characteristic. For this, we introduce a notion of relative Hodge sheaves and study their behavior under blow-ups along smooth centers. In particular, as an application, we study the blow-up invariance of the E₂-degeneracy of the Hochschild--Kostant--Rosenberg spectral sequence for smooth proper varieties.

Cited by

• Counterexamples to Hochschild--Kostant--Rosenberg in characteristic p
• On the Morse--Novikov Cohomology of blowing up complex manifolds

Related

• On the blow-up formula of twisted de Rham cohomology
• Blow-up invariance for Hodge-Witt sheaves with modulus
• Hodge number polynomials for nearby and vanishing cohomology
• Dolbeault cohomologies of blowing up complex manifolds II: bundle-valued case
• A bound on the Hodge filtration of the de Rham cohomology of supervarieties