Geodesic
A~new series of moduli components of rank-2 semistable sheaves on~$\mathbb{P}^{3}$ with singularities of mixed dimension
Sbornik. Mathematics, Tome 211 (2020) no. 7, pp. 967-986

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We construct a new infinite series of irreducible components of the Gieseker-Maruyama moduli scheme $\mathscr{M}(k)$, $k \geqslant 3$, of semistable rank-2 sheaves on $\mathbb{P}^3$ with Chern classes $c_1=0$, $c_2=k$ and $c_3=0$, whose general points are sheaves with singularities of mixed dimension. These sheaves are constructed by elementary transformations of stable and properly $\mu$-semistable reflexive sheaves along disjoint unions of collections of points and smooth irreducible curves which are rational or complete intersection curves in $\mathbb{P}^{3}$. As a special member of this series, we obtain a new component of $\mathscr{M}(3)$. Bibliography: 12 titles.
Keywords: rank-2 semistable sheaves, reflexive sheaves
Mots-clés : moduli spaces. 
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     author = {A. N. Ivanov},
     title = {A~new series of moduli components of rank-2 semistable sheaves on~$\mathbb{P}^{3}$ with singularities of mixed dimension},
     journal = {Sbornik. Mathematics},
     pages = {967--986},
     publisher = {mathdoc},
     volume = {211},
     number = {7},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2020_211_7_a3/}
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A. N. Ivanov. A~new series of moduli components of rank-2 semistable sheaves on~$\mathbb{P}^{3}$ with singularities of mixed dimension. Sbornik. Mathematics, Tome 211 (2020) no. 7, pp. 967-986. http://geodesic.mathdoc.fr/item/SM_2020_211_7_a3/