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A new series of moduli components of rank-2 semistable sheaves on \({\mathbb{P}}^3\) with singularities of mixed dimension. (English. Russian original) Zbl 1451.14031

Sb. Math. 211, No. 7, 967-986 (2020); translation from Mat. Sb. 211, No. 7, 72-92 (2020).
Let \(\mathcal{M}(k)\), \(k\ge 3\), denote the Gieseker-Maruyama moduli scheme of rank \(2\) torsion free sheaves on \(\mathbb {P}^3\) with \(c_1=0\), \(c_2=k\) and \(c_3=0\). Here (using elementary transformation) the author construct new irreducible components of \(\mathcal {M}(k)\) improving and generalizing [A. N. Ivanov and A. S. Tikhomorov, J. Geom. Phys. 129, 90–98 (2018; Zbl 1467.14030); M. Jardin et al., Mosc. Math. J. 18, No. 1, 117–148 (2018; Zbl 1439.14047)], [M. Jardin et al., Ann. Mat. Pura Appl. (4) 196, No. 4 (2017; Zbl 1481.14020)]. In particular the author constructs a new component of \(\mathcal {M}(3)\).

MSC:

14D20 Algebraic moduli problems, moduli of vector bundles
14J60 Vector bundles on surfaces and higher-dimensional varieties, and their moduli
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References:

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