Mark Andrea A. de Cataldo
Stony Brook University
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Publication
Featured researches published by Mark Andrea A. de Cataldo.
Journal of Algebraic Geometry | 2011
Mark Andrea A. de Cataldo
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.
Archive | 2007
Mark Andrea A. de Cataldo
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.
Proceedings of the American Mathematical Society | 2009
Mark Andrea A. de Cataldo; Luca Migliorini
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.
Compositio Mathematica | 2017
Mark Andrea A. de Cataldo
We prove that the direct image complex for the
Mathematische Zeitschrift | 2018
Mark Andrea A. de Cataldo; Thomas J. Haines; Li Li
D
Annales Scientifiques De L Ecole Normale Superieure | 2005
Mark Andrea A. de Cataldo; Luca Migliorini
-twisted
Annals of Mathematics | 2012
Mark Andrea A. de Cataldo; Tamas Hausel; Luca Migliorini
SL_n
Journal of Algebra | 2002
Mark Andrea A. de Cataldo; Luca Migliorini
Hitchin fibration is determined by its restriction to the elliptic locus, where the spectral curves are integral. The analogous result for
Annales Scientifiques De L Ecole Normale Superieure | 2002
Mark Andrea A. de Cataldo; Luca Migliorini
GL_n
Mathematical Research Letters | 2004
Mark Andrea A. de Cataldo; Luca Migliorini
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