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Sibirskii Matematicheskii Zhurnal, 2014, Volume 55, Number 6, Pages 1396–1403 (Mi smj2614)  

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
Full-text PDF (316 kB) Citations (3)
References:
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
English version:
Siberian Mathematical Journal, 2014, Volume 55, Issue 6, Pages 1137–1143
DOI: https://doi.org/10.1134/S0037446614060172
Bibliographic databases:
Document Type: Article
UDC: 512.723
Language: Russian
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
Citation in format AMSBIB
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\by S.~A.~Tikhomirov
\paper Families of stable bundles of rank~2 with $c_1=-1$ on the space~$\mathbb P^3$
\jour Sibirsk. Mat. Zh.
\yr 2014
\vol 55
\issue 6
\pages 1396--1403
\mathnet{http://mi.mathnet.ru/smj2614}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3330045}
\transl
\jour Siberian Math. J.
\yr 2014
\vol 55
\issue 6
\pages 1137--1143
\crossref{https://doi.org/10.1134/S0037446614060172}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84919461390}
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  • https://www.mathnet.ru/eng/smj/v55/i6/p1396
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Сибирский математический журнал Siberian Mathematical Journal
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