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Given the data (X,L, ζ) where X is a smooth 2n-dimensional algebraic variety, L → X is a very ample line bundle and ζ ∈ Hg(X)prim is a primitive Hodge class, we shall define an analytic invariant
This paper investigates the Hodge theory of proper algebraic maps f : X → Y of complex algebraic varieties and its topological implications. The key case is when X and Y are projective and X is… (More)
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… (More)
We compute the Chow motive and the Chow groups with rational coefficients of the Hilbert scheme of points on a smooth algebraic surface.
Let G be a complex reductive group acting algebraically on a complex projective variety X . Given a polarisation of X , i.e., an ample G-line bundle L over X , Mumford (see [M-F-K]) defined the… (More)
Osseous choristoma is a normal bone tissue in an ectopic position. In the oral region lingual localization occurs more frequently and the mass is generally localized on the dorsum of the tongue.… (More)
We describe the perverse filtration in cohomology using the Lefschetz hyperplane theorem.
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 Hodge-Riemann… (More)
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 to show how the… (More)
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 rational… (More)