Displaying similar documents to “Symplectic structures on moduli spaces of framed sheaves on surfaces”

Algebraic complete integrability of an integrable system of Beauville

Jun-Muk Hwang, Yasunari Nagai (2008)

Annales de l’institut Fourier

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We show that the Beauville’s integrable system on a ten dimensional moduli space of sheaves on a K3 surface constructed via a moduli space of stable sheaves on cubic threefolds is algebraically completely integrable, using O’Grady’s construction of a symplectic resolution of the moduli space of sheaves on a K3.

On the Brill-Noether theory for K3 surfaces

Maxim Leyenson (2012)

Open Mathematics

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Let (S, H) be a polarized K3 surface. We define Brill-Noether filtration on moduli spaces of vector bundles on S. Assume that (c 1(E), H) > 0 for a sheaf E in the moduli space. We give a formula for the expected dimension of the Brill-Noether subschemes. Following the classical theory for curves, we give a notion of Brill-Noether generic K3 surfaces. Studying correspondences between moduli spaces of coherent sheaves of different ranks on S, we prove our main theorem: polarized K3...

On moduli spaces of semistable sheaves on Enriques surfaces

Marcin Hauzer (2010)

Annales Polonici Mathematici

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We describe some one-dimensional moduli spaces of rank 2 Gieseker semistable sheaves on an Enriques surface improving earlier results of H. Kim. In the case of a nodal Enriques surface the moduli spaces obtained are reducible for general polarizations. For unnodal Enriques surfaces we show how to reduce the study of moduli spaces of high even rank Gieseker semistable sheaves to low ranks. To prove this we use the method of K. Yoshioka who showed that in the odd rank case, one can reduce...