The combinatorial part of the cohomology of a singular variety

Abstract

We study the first step of the weight filtration on the cohomology of a proper complex algebraic variety, which we call the combinatorial part. We obtain a natural upper bound on its size, which gives rather strong information about the topology of rational singularities.

arXiv comment9 pages

References in corpus (1)

• On the cohomology of a simple normal crossings divisor

Cited by in corpus (5)

• Cohomological Hasse principle and resolution of quotient singularities
• Boundary complexes and weight filtrations
• Weights on cohomology, invariants of singularities, and dual complexes
• Equisingular resolution with SNC fibers and combinatorial type of varieties
• Hodge-Deligne equivariant polynomials and monodromy of hyperplane arrangements