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A support theorem for Hilbert schemes of planar curves

Luca Migliorini, Vivek 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...

Abelian surfaces and products of elliptic curves

Marina Rosanna Marchisio (1998)

Bollettino dell'Unione Matematica Italiana

Si dà una nuova e completa dimostrazione del risultato cruciale del metodo di Ruppert che consente di stabilire in maniera effettiva quando una superficie abeliana è isomorfa o isogena a un prodotto di curve ellittiche.

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