Geodesic
On the Hilbert scheme of the moduli space of torsion-free sheaves on surfaces
Glasgow mathematical journal, Tome 65 (2023) no. 2, pp. 414-429

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DOI

The aim of this paper is to determine a bound of the dimension of an irreducible component of the Hilbert scheme of the moduli space of torsion-free sheaves on surfaces. Let X be a nonsingular irreducible complex surface, and let E be a vector bundle of rank n on X. We use the m-elementary transformation of E at a point $x \in X$ to show that there exists an embedding from the Grassmannian variety $\mathbb{G}(E_x,m)$ into the moduli space of torsion-free sheaves $\mathfrak{M}_{X,H}(n;\,c_1,c_2+m)$ which induces an injective morphism from $X \times M_{X,H}(n;\,c_1,c_2)$ to $Hilb_{\, \mathfrak{M}_{X,H}(n;\,c_1,c_2+m)}$.
DOI : 10.1017/S0017089523000010
Mots-clés : elementary transformation, moduli of vector bundles, moduli of sheaves, Hilbert scheme 
Mata-Gutiérrez, O.; Roa-Leguizamón, L.; Torres-López, H. On the Hilbert scheme of the moduli space of torsion-free sheaves on surfaces. Glasgow mathematical journal, Tome 65 (2023) no. 2, pp. 414-429. doi: 10.1017/S0017089523000010
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     title = {On the {Hilbert} scheme of the moduli space of torsion-free sheaves on surfaces},
     journal = {Glasgow mathematical journal},
     pages = {414--429},
     year = {2023},
     volume = {65},
     number = {2},
     doi = {10.1017/S0017089523000010},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089523000010/}
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