4 citations · 5 across the 4 of their papers we have counts for
10 papers · 1 filter
Lectures on the Hodge theory of projective manifolds
Mark A. de Cataldo
This is a written-up version of eight introductory lectures to the Hodge theory of projective manifolds. The table of contents should be self-explanatory. The only exception is sec…
The Gysin map is compatible with mixed Hodge structures
Mark A. de Cataldo, Luca Migliorini
We prove that the Gysin map is compatible with mixed Hodge Structures.
Intersection forms, topology of maps and motivic decomposition for maps of threefolds
Mark Andrea A. de Cataldo, Luca Migliorini
This paper has two aims. The former is to give an introduction to our earlier work on the Hodge theory of algebraic maps and more generally to some of the main themes of the theory…
The Hodge theory of algebraic maps
Mark Andrea A. de Cataldo, Luca Migliorini
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 map of…
The Chow motive of semismall resolutions
Mark Andrea A. de Cataldo, Luca Migliorini
We consider proper, algebraic semismall maps f from a complex algebraic manifold X. We show that the topological Decomposition Theorem implies a "motivic" decomposition theorem for…
The Hard Lefschetz Theorem and the topology of semismall maps
Mark Andrea de Cataldo, Luca Migliorini
We introduce the notion of lef line bundles on a complex projective manifold. We prove that lef line bundles satisfy the Hard Lefschetz Theorem, the Lefschetz Decomposition and the…