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Construction of stable rank $2$ bundles on $\mathbb{P}^3$ via symplectic bundles
A. S. Tikhomirova,
S. A. Tikhomirovbc,
D. A. Vassilieva a National Research University Higher School of Economics, Moscow, Russia
b Yaroslavl State Pedagogical University named after K. D. Ushinskii, Yaroslavl, Russia
c Koryazhma Branch of Northern (Arctic) Federal University named after M. V. Lomonosov, Koryazhma, Russia
Abstract:
In this article we study the Gieseker–Maruyama moduli spaces
$\mathcal{B}(e, n)$ of stable rank
$2$ algebraic vector bundles with Chern classes
$c_1 = e \in \{-1, 0\}$ and
$c_2 = n \geqslant 1$ on the projective space
$\mathbb{P}^3$. We construct the two new infinite series
$\Sigma_0$ and
$\Sigma_1$ of irreducible components of the spaces
$\mathcal{B}(e, n)$ for
$e = 0$ and
$e = -1$, respectively. General bundles of these components are obtained as cohomology sheaves of monads whose middle term is a rank
$4$ symplectic instanton bundle in case
$e = 0$, respectively, twisted symplectic bundle in case
$e = -1$. We show that the series
$\Sigma_0$ contains components for all big enough values of n (more precisely, at least for
$n \geqslant 146$).
$\Sigma_0$ yields the next example, after the series of instanton components, of an infinite series of components of
$\mathcal{B}(0, n)$ satisfying this property.
Keywords:
rank $2$ bundles, moduli of stable bundles, symplectic bundles.
UDC:
512.7
MSC: 35R30 Received: 12.04.2018
Revised: 25.11.2018
Accepted: 19.12.2018
DOI:
10.33048/smzh.2019.60.215
Fulltext:
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