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Displaying similar documents to “K3 surfaces: moduli spaces and Hilbert schemes.”

Symplectic structures on moduli spaces of framed sheaves on surfaces

Francesco Sala (2012)

Open Mathematics

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We provide generalizations of the notions of Atiyah class and Kodaira-Spencer map to the case of framed sheaves. Moreover, we construct closed two-forms on the moduli spaces of framed sheaves on surfaces. As an application, we define a symplectic structure on the moduli spaces of framed sheaves on some birationally ruled surfaces.

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...

Rank-two vector bundles on Hirzebruch surfaces

Marian Aprodu, Vasile Brînzănescu, Marius Marchitan (2012)

Open Mathematics

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We survey some parts of the vast literature on vector bundles on Hirzebruch surfaces, focusing on the rank-two case.

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...

On rank 2 semistable vector bundles over an irreducible nodal curve of genus 2

Sonia Brivio (1998)

Bollettino dell'Unione Matematica Italiana

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Sia C una curva irriducibile nodale di genere aritmetico p a = 2 . In queste note vogliamo mostrare come il sistema lineare delle quadriche, contenenti un opportuno modello proiettivo della curva, permette di descrivere i fibrati vettoriali semistabili, di rango 2 , su C .