Abstract:
Moduli of stable rank 2 vector bundles on the three-dimensional complex projective space are studied. Using the notion of spectrum, two series of components in the moduli scheme of such bundles are pointed out. Each component is an irreducible rational variety, and asymptotically the dimension of the components behaves as a quadratic or cubic polynomial. The monadic realization of a generic bundle on the components is given by a rank one monad.
Bibliography: 5 titles.
\Bibitem{Ved84}
\by V.~K.~Vedernikov
\paper Moduli of stable vector bundles of rank~2 on $P_3$ with fixed spectrum
\jour Math. USSR-Izv.
\yr 1985
\vol 25
\issue 2
\pages 301--313
\mathnet{http://mi.mathnet.ru/eng/im1504}
\crossref{https://doi.org/10.1070/IM1985v025n02ABEH001282}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=764306}
\zmath{https://zbmath.org/?q=an:0589.14017}
Linking options:
https://www.mathnet.ru/eng/im1504
https://doi.org/10.1070/IM1985v025n02ABEH001282
https://www.mathnet.ru/eng/im/v48/i5/p986
This publication is cited in the following 8 articles:
D. A. Vasil'ev, A. S. Tikhomirov, “Moduli of rank $2$ semistable sheaves on rational Fano threefolds of the main series”, Sb. Math., 215:10 (2024), 1269–1320
A. A. Kytmanov, N. N. Osipov, S. A. Tikhomirov, T. V. Zykova, “O chislovykh kharakteristikakh nekotorykh rassloenii i ikh prostranstva modulei na $\mathbb{P}^3$”, Sib. elektron. matem. izv., 19:2 (2022), 415–425
Charles Almeida, Marcos Jardim, Alexander S. Tikhomirov, “Irreducible components of the moduli space of rank 2 sheaves of odd determinant on projective space”, Advances in Mathematics, 402 (2022), 108363
A. S. Tikhomirov, S. A. Tikhomirov, D. A. Vassiliev, “Construction of stable rank $2$ bundles on $\mathbb{P}^3$ via symplectic bundles”, Siberian Math. J., 60:2 (2019), 343–358
Kytmanov A.A. Tikhomirov A.S. Tikhomirov S.A., “Series of Rational Moduli Components of Stable Rank Two Vector Bundles on P-3”, Sel. Math.-New Ser., 25:2 (2019), UNSP 29
N. N. Osipov, S. A. Tikhomirov, “On the number of Vedernikov–Ein irreducible components of the moduli space of stable rank 2 bundles on the projective space”, Siberian Math. J., 59:1 (2018), 107–112
A. A. Kytmanov, N. N. Osipov, S. A. Tikhomirov, “Finding ein components in the moduli spaces of stable rank $2$ bundles on the projective $3$-space”, Siberian Math. J., 57:2 (2016), 322–329
S. A. Tikhomirov, “Families of stable bundles of rank 2 with $c_1=-1$ on the space $\mathbb P^3$”, Siberian Math. J., 55:6 (2014), 1137–1143
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