Abstract
We construct some infinite series of families of stable rank 2 vector bundles on the projective space ℙ3 with odd first Chern class c 1 = −1 and arbitrary second Chern class c 2 = 2n with n ≥ 2. They are distinct from the series of families of bundles which were constructed by Hartshorne in 1978. We conjecture that for n ≥ 3 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 ℙ3 has at least two irreducible components.
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Original Russian Text Copyright © 2014 Tikhomirov S.A.
The author was partially supported by the Ministry of Education and Science of the Russian Federation.
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 55, No. 6, pp. 1396–1403, November–December, 2014.
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Tikhomirov, S.A. Families of stable bundles of rank 2 with c 1 =−1 on the space ℙ3 . Sib Math J 55, 1137–1143 (2014). https://doi.org/10.1134/S0037446614060172
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DOI: https://doi.org/10.1134/S0037446614060172