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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...

About G -bundles over elliptic curves

Yves Laszlo (1998)

Annales de l'institut Fourier

Let G be a complex algebraic group, simple and simply connected, T a maximal torus and W the Weyl group. One shows that the coarse moduli space M G ( X ) parametrizing S -equivalence classes of semistable G -bundles over an elliptic curve X is isomorphic to [ Γ ( T ) ⊗ Z X ] / W . By a result of Looijenga, this shows that M G ( X ) is a weighted projective space.

ACM bundles on general hypersurfaces in P5 of low degree.

Luca Chiantini, Carlo K. Madonna (2005)

Collectanea Mathematica

In this paper we show that on a general hypersurface of degree r = 3,4,5,6 in P5 a rank 2 vector bundle ε splits if and only if h1ε(n) = h2ε(n) = 0 for all n ∈ Z. Similar results for r = 1,2 were obtained in [15], [16] and [2].

ACM bundles, quintic threefolds and counting problems

N. Mohan Kumar, Aroor Rao (2012)

Open Mathematics

We review some facts about rank two arithmetically Cohen-Macaulay bundles on quintic threefolds. In particular, we separate them into seventeen natural classes, only fourteen of which can appear on a general quintic. We discuss some enumerative problems arising from these.

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