Remarks on a conjecture of Hartshorne.
Ricordo di Paolo de Bartolomeis
A support theorem for Hilbert schemes of planar curves
Consider a family of integral complex locally planar curves whose relative Hilbert scheme of points is smooth. The decomposition theorem of Beilinson, Bernstein, and Deligne asserts that the pushforward of the constant sheaf on the relative Hilbert scheme splits as a direct sum of shifted semisimple perverse sheaves. We will show that no summand is supported in positive codimension. It follows that the perverse filtration on the cohomology of the compactified Jacobian of an integral plane curve...
Semistable quotients
The hard Lefschetz theorem and the topology of semismall maps
The Hodge theory of algebraic maps
Propriétés globales de l'espace de twisteurs
We study global properties of the twistor space over an even dimensional conformally flat manifold, proving that the twistor space is Kähler if and only if the manifold is conformally equivalent to the standard -dimensional sphere ().
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