K3 surfaces: moduli spaces and Hilbert schemes

• Autores: Laura Costa Farràs
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 49, Fasc. 2-3, 1998, págs. 273-282
• Idioma: inglés
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• Resumen

  • Let $X$ be an algebraic $K3$ surface. Fix an ample divisor $H$ on $X,L\in Pic(X)$ and $c_2\in\mathbb{Z}$. Let $M_H(r; L, c_2)$ be the moduli space of rank $r,H$-stable vector bundles $E$ over $X$ with det($E) = L$ and $c_2(E) = c_2$. The goal of this paper is to determine invariants ($r; c_1, c_2$) for which $M_H(r; L, c_2)$ is birational to some Hilbert scheme $Hilb^l(X)$.