Mark Andrea A. de Cataldo

The perverse filtration and the Lefschetz hyperplane theorem, II

The perverse filtration in cohomology and in cohomology with compact supports is interpreted in terms of kernels of restrictions maps to suitable subvarieties by using the Lefschetz hyperplane theorem and spectral objects. Various mixed-Hodge-theoretic consequences for intersection cohomology and for the decomposition theorem are derived.

The Hodge theory of projective manifolds

Calculus on Smooth Manifolds The Hodge Theory of a Smooth, Compact, Oriented, Riemannian Manifold Complex Manifolds Hermitean Linear Algebra Hermitean Manifolds Kahler Manifolds The Hard Lefschetz Theorem and the Hodge-Riemann Bilinear Relations Mixed Hodge Structures, Semi-Simplicity and Approximation.

On singularities of primitive cohomology classes

Green and Griffiths have introduced several notions of singularities associated with normal functions, especially in connection with middle-dimensional primitive Hodge classes. In this paper, by using the more elementary aspects of the Decomposition Theorem, we define global and local singularities associated with primitive middle-dimensional cohomology classes, and by using the Relative Hard Lefschetz Theorem, we show that these singularities detect the global and local triviality of the primitive class.

A support theorem for the Hitchin fibration: the case of

We prove that the direct image complex for the

Frobenius semisimplicity for convolution morphisms

D

The Hodge theory of algebraic maps

-twisted

Topology of Hitchin systems and Hodge theory of character varieties: the case A1

SL_n

The Chow Groups and the Motive of the Hilbert Scheme of Points on a Surface

Hitchin fibration is determined by its restriction to the elliptic locus, where the spectral curves are integral. The analogous result for

The hard Lefschetz theorem and the topology of semismall maps

GL_n

The Chow motive of semismall resolutions

is due to P.-H. Chaudouard and G. Laumon. Along the way, we prove that the Tate module of the relative Prym group scheme is polarizable, and we also prove