12 citations · 64 across the 31 of their papers we have counts for
35 papers
Perverse Leray filtration and specialization with applications to the Hitchin morphism
MArk Andrea A de Cataldo
We initiate and develop a framework to handle the specialization morphism as a filtered morphism for the perverse, and for the perverse Leray filtration, on the cohomology with con…
On the P=W conjecture for
Mark Andrea A. de Cataldo, Davesh Maulik, Junliang Shen
Let be a prime number. We prove that the conjecture for is equivalent to the conjecture for . As a consequence, we verify the c…
Compactification of Dolbeault moduli spaces
Mark Andrea A. de Cataldo
We construct a relative compactification of Dolbeault moduli spaces of Higgs bundles for reductive algebraic groups on families of projective manifolds that is compatible with the…
The perverse filtration for the Hitchin fibration is locally constant
Mark Andrea A. de Cataldo, Davesh Maulik
We prove that the perverse Leray filtration for the Hitchin morphism is locally constant in families, thus providing some evidence towards the validity of the conjecture due…
Decomposition theorem for semi-simples
Mark Andrea de Cataldo
We use standard constructions in algebraic geometry and homological algebra to extend the decomposition and hard Lefschetz theorems of T. Mochizuki and C. Sabbah so that they remai…
Perverse sheaves and the topology of algebraic varieties (2015 PCMI)
Mark Andrea A. de Cataldo
Another introduction to perverse sheaves with some exercises. Expanded version of five lectures at the 2015 PCMI.