Boundary complexes and weight filtrations

By Sam Payne. 2011

60 citations recorded by the source corpus.

We study the dual complexes of boundary divisors in log resolutions of compactifications of algebraic varieties and show that the homotopy types of these complexes are independent of all choices. Inspired by recent developments in nonarchimedean geometry, we consider relations between these boundary complexes and weight filtrations on singular cohomology and cohomology with compact supports, and give applications to dual complexes of resolutions of isolated singularities that generalize results of Stepanov and Thuillier.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/86587a9451a7e5ee77fd3cb155035c1385dd8b25

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. David Anderson
2. Sam Payne
3. Eric Katz
4. David Jensen
5. Kiumars Kaveh
6. Dhruv Ranganathan
7. Matthew Baker
8. Walter Gubler

In Mathematical Physics

1. David Anderson
2. Sam Payne

Citations in the corpus

• Operational K-Theory (2013, background): “Let ∆( E ) be the dual complex of E , i.e. the ∆-complex with one vertex for each irreducible component of E , one edge for each component of a pairwise intersection, and so on, as described in [Pa3, § 2].”