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Modelirovanie i Analiz Informatsionnykh Sistem, 2014, Volume 21, Number 2, Pages 90–96
(Mi mais373)
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Reducibility of the Moduli Space of Stable Rank $2$ Reflexive Sheaves with Chern Classes $c_1=-1$, $c_2=4$, $c_3=2$ on Projective Space $\mathbb{P}^3$
A. S. Tikhomirov, M. A. Zavodchikov Yaroslavl State Pedagogical University named after K. D. Ushinsky, Respublikanskaya st., 108, Yaroslavl, 150000, Russia
Abstract:
We prove the reducibility of the moduli space $M_{\mathbb{P}^3}^{\mathrm{ref}}(2;-1,4,2)$ of stable rank 2 reflexive sheaves with Chern classes $c_1=-1$, $c_2=4$, $c_3=2$ on projective space $\mathbb {P}^3$. This gives the first example of a reducible space in the series of moduli spaces of stable rank 2 reflexive sheaves with Chern classes $c_1=-1$, $c_2=4$, $c_3=2m$, $m=1,2,3,4,5,6,8$. We find two components of the expected dimension 27 of this space and give their geometric description via the Serre construction.
Keywords:
moduli space, stable reflexive sheaf, Serre construction.
Received: 14.04.2014
Citation:
A. S. Tikhomirov, M. A. Zavodchikov, “Reducibility of the Moduli Space of Stable Rank $2$ Reflexive Sheaves with Chern Classes $c_1=-1$, $c_2=4$, $c_3=2$ on Projective Space $\mathbb{P}^3$”, Model. Anal. Inform. Sist., 21:2 (2014), 90–96
Linking options:
https://www.mathnet.ru/eng/mais373 https://www.mathnet.ru/eng/mais/v21/i2/p90
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Abstract page: | 244 | Full-text PDF : | 89 | References: | 46 |
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