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A support theorem for Hilbert schemes of planar curves

Luca MiglioriniVivek Shende — 2013

Journal of the European Mathematical Society

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...

Propriétés globales de l'espace de twisteurs

Paolo De BartolomeisLuca MiglioriniAntonella Nannicini — 1991

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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 2 n -dimensional sphere ( n > 2 ).

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