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Sibirskii Matematicheskii Zhurnal, 2014, Volume 55, Number 6, Pages 1396–1403
(Mi smj2614)
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This article is cited in 3 scientific papers (total in 3 papers)
Families of stable bundles of rank 2 with $c_1=-1$ on the space $\mathbb P^3$
S. A. Tikhomirovab a Yaroslavl' State Pedagogical University, Yaroslavl', Russia
b Koryazhma Branch of Northern (Arctic) Federal University, Koryazhma, Russia
Abstract:
We construct some infinite series of families of stable rank 2 vector bundles on the projective space $\mathbb P^3$ with odd first Chern class $c_1=-1$ and arbitrary second Chern class $c_2=2n$ with $n\ge2$. They are distinct from the series of families of bundles which were constructed by Hartshorne in 1978. We conjecture that for $n\ge3$ these families lie in the irreducible components of the moduli space of stable bundles distinct from the components that include Hartshorne's families. In this article we prove the conjecture for $n=3$. In this case the scheme of moduli of stable rank 2 vector bundles with $c_1=-1$ and $c_2=6$ on $\mathbb P^3$ has at least two irreducible components.
Keywords:
vector bundle, family, moduli space.
Received: 20.03.2014
Citation:
S. A. Tikhomirov, “Families of stable bundles of rank 2 with $c_1=-1$ on the space $\mathbb P^3$”, Sibirsk. Mat. Zh., 55:6 (2014), 1396–1403; Siberian Math. J., 55:6 (2014), 1137–1143
Linking options:
https://www.mathnet.ru/eng/smj2614 https://www.mathnet.ru/eng/smj/v55/i6/p1396
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Abstract page: | 228 | Full-text PDF : | 70 | References: | 39 | First page: | 3 |
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