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New moduli components of rank 2 bundles on projective space. (English. Russian original) Zbl 1542.14015

Sb. Math. 212, No. 11, 1503-1552 (2021); translation from Mat. Sb. 212, No. 11, 3-54 (2021).
Let \(X\) be a projective scheme, and \({\mathcal{B}}_X(r, c_1,\ldots,c_r)\) the Maruyama scheme that parameterizes stable holomorphic vector bundles on \(X\) of fixed rank \(r\) and Chern classes \(c_1,\ldots,c_r\).
C. Almeida, M. Jardim, A. S. Tikhomirov, and S. A. Tikhomirov study the moduli spaces \({\mathcal{B}}(n)={\mathcal{B}}_{{\mathbb{P}}^3}(2,0,n)\) for \(n\geq 5\). The first main theorem deals with the part of \({\mathcal{B}}(n)\) which arises from certain monads for \(n=a^2+1\), \(a\geq 2\) and \(a\neq3\). It is shown to contain rational components of dimension \(4\binom{a+3}{3}-a-1\).
The second theorem states that \({\mathcal{B}}(5)\) consists of exactly two irreducible components of dimension \(37\) and one further component of dimension \(40\).
The authors give detailed references to related known results.

MSC:

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

References:

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