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1998

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/16925

K3 surfaces: moduli spaces and Hilbert schemes

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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 $Hilb^l(X)$.

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Esquemes de Hilbert, Teoria de mòduls, Superfícies algebraiques

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Hilbert schemes, Moduli theory, Algebraic surfaces

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COSTA FARRÀS, Laura. K3 surfaces: moduli spaces and Hilbert schemes. Collectanea Mathematica. 1998. Vol. 49, num. 2-3, pags. 273-282. ISSN 0010-0757. [consulted: 15 of October of 2026]. Available at: https://hdl.handle.net/2445/16925

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