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 …
decomposition theorem of Beilinson, Bernstein, Deligne and Gabber. A goal of this survey is …
[PDF][PDF] The Hodge theory of algebraic maps
MAA de Cataldo, L Migliorini - Annales scientifiques de l'Ecole normale …, 2005 - numdam.org
We give a geometric proof of the Decomposition Theorem of Beilinson, Bernstein, Deligne
and Gabber for the direct image of the intersection cohomology complex under a proper …
and Gabber for the direct image of the intersection cohomology complex under a proper …
Motivic hyper-Kähler resolution conjecture, I: generalized Kummer varieties
Given a smooth projective variety M endowed with a faithful action of a finite group G,
following Jarvis–Kaufmann–Kimura (Invent. Math. 168 (2007) 23–81), and Fantechi …
following Jarvis–Kaufmann–Kimura (Invent. Math. 168 (2007) 23–81), and Fantechi …
On the Chow theory of projectivizations
Q Jiang - Journal of the Institute of Mathematics of Jussieu, 2023 - cambridge.org
In this paper, we prove a decomposition result for the Chow groups of projectivizations of
coherent sheaves of homological dimension. In this process, we establish the …
coherent sheaves of homological dimension. In this process, we establish the …
On the motive of O'Grady's ten-dimensional hyper-Kähler varieties
S Floccari, L Fu, Z Zhang - Communications in Contemporary …, 2021 - World Scientific
We investigate how the motive of hyper-Kähler varieties is controlled by weight-2 (or surface-
like) motives via tensor operations. In the first part, we study the Voevodsky motive of …
like) motives via tensor operations. In the first part, we study the Voevodsky motive of …
Distinguished cycles on varieties with motive of abelian type and the section property
A remarkable result of Peter O'Sullivan asserts that the algebra epimorphism from the
rational Chow ring of an abelian variety to its rational Chow ring modulo numerical …
rational Chow ring of an abelian variety to its rational Chow ring modulo numerical …
Cohomology of the Hilbert scheme of points on a surface with values in representations of tautological bundles
L Scala - Duke Mathematical Journal, 2009 - projecteuclid.org
Let X [n] be the Hilbert scheme of n points on the smooth quasi-projective surface X, and let
L [n] be the tautological bundle on X [n] naturally associated to the line bundle L on X. As a …
L [n] be the tautological bundle on X [n] naturally associated to the line bundle L on X. As a …
On the interior motive of certain Shimura varieties: the case of Picard surfaces
J Wildeshaus - Manuscripta mathematica, 2015 - Springer
The purpose of this article is to construct a Hecke-equivariant Chow motive whose
realizations equal interior (or intersection) cohomology of Picard surfaces with regular …
realizations equal interior (or intersection) cohomology of Picard surfaces with regular …
[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 …
2016 IAS/Park City Mathematics Series Volume 00, Pages 000–000 S 1079-5634(XX)0000-0 …
The Hodge theory of the Decomposition Theorem (after de Cataldo and Migliorini)
G Williamson - arXiv preprint arXiv:1603.09235, 2016 - arxiv.org
In its simplest form the Decomposition Theorem asserts that the rational intersection
cohomology of a complex projective variety occurs as a summand of the cohomology of any …
cohomology of a complex projective variety occurs as a summand of the cohomology of any …