Jumping conics on a smooth quadric in $${\mathbb {P}_3}$$ |
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Authors: | Sukmoon Huh |
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Institution: | 1.Korea Institute for Advanced Study,Seoul,Korea |
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Abstract: | We investigate the jumping conics of stable vector bundles E of rank 2 on a smooth quadric surface Q with the first Chern class c1 = OQ(-1,-1){c_1= \mathcal{O}_Q(-1,-1)} with respect to the ample line bundle OQ(1,1){\mathcal {O}_Q(1,1)} . We show that the set of jumping conics of E is a hypersurface of degree c
2(E) − 1 in
\mathbb P3*{\mathbb {P}_3^{*}} . Using these hypersurfaces, we describe moduli spaces of stable vector bundles of rank 2 on Q in the cases of lower c
2(E). |
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Keywords: | |
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