The decomposition theorem, perverse sheaves and the topology of algebraic maps

M de Cataldo, L Migliorini - Bulletin of the American Mathematical Society, 2009 - ams.org
We give a motivated introduction to the theory of perverse sheaves, culminating in the
decomposition theorem of Beilinson, Bernstein, Deligne and Gabber. A goal of this survey is …

[图书][B] Intersection Homology & Perverse Sheaves

L Maxim - 2019 - Springer
In recent years, intersection homology and perverse sheaves have become indispensable
tools for studying the topology of singular spaces. This book provides a gentle introduction to …

[PDF][PDF] Perverse sheaves and the topology of algebraic varieties (2015 PCMI)

MAA de Cataldo - arXiv preprint arXiv:1506.03642, 2015 - arxiv.org
arXiv:1506.03642v2 [math.AG] 14 Nov 2016 Page 1 arXiv:1506.03642v2 [math.AG] 14 Nov
2016 IAS/Park City Mathematics Series Volume 00, Pages 000–000 S 1079-5634(XX)0000-0 …

Multiplicativity of perverse filtration for Hilbert schemes of fibered surfaces

Z Zhang - Advances in Mathematics, 2017 - Elsevier
Abstract Let S→ C be a smooth projective surface with numerically trivial canonical bundle
fibered onto a curve. We prove the multiplicativity of the perverse filtration with respect to the …

Perverse filtrations, Hilbert schemes, and the P= W conjecture for parabolic Higgs bundles

J Shen, Z Zhang - arXiv preprint arXiv:1810.05330, 2018 - arxiv.org
We prove de Cataldo-Hausel-Migliorini's P= W conjecture in arbitrary rank for parabolic
Higgs bundles labeled by the affine Dynkin diagrams $\tilde {A} _0 $, $\tilde {D} _4 $, $\tilde …

The identity for cluster varieties

Z Zhang - arXiv preprint arXiv:1903.07014, 2019 - arxiv.org
We find new examples of the $ P= W $ identity of de Cataldo-Hausel-Migliorini by studying
cluster varieties. We prove that the weight filtration of 2D cluster varieties correspond to the …

Local vanishing and Hodge filtration for rational singularities

M Mustaţă, S Olano, M Popa - Journal of the Institute of Mathematics …, 2020 - cambridge.org
LOCAL VANISHING AND HODGE FILTRATION FOR RATIONAL SINGULARITIES Page 1 J.
Inst. Math. Jussieu (2020) 19(3), 801–819 doi:10.1017/S1474748018000208 c Cambridge …

Hodge-theoretic aspects of the decomposition theorem

MAA de Cataldo, L Migliorini - 2006 - books.google.com
Given a projective morphism of compact, complex, algebraic varieties and a relatively ample
line bundle on the domain we prove that a suitable choice, dictated by the line bundle, of the …

The Duistermaat-Heckman formula and the cohomology of moduli spaces of polygons

A Mandini - 2014 - projecteuclid.org
We give a presentation of the cohomology ring of spatial polygon spaces M(r) with fixed side
lengths r∈R^n_+. These spaces can be described as the symplectic reduction of the …

On the existence of a Gysin morphism for the Blow-up of an ordinary singularity

V Di Gennaro, D Franco - ANNALI DELL'UNIVERSITA'DI FERRARA, 2017 - Springer
In this paper we characterize the Blowing-up maps of ordinary singularities for which there
exists a natural Gysin morphism, ie a bivariant class θ ∈ Hom_ D (Y)(R π _* Q _X, Q _Y) θ∈ …