Jumping conics on a smooth quadric in $\PP_3$

Details Jumping conics on a smooth quadric in $\PP_3$ Jumping conics on a smooth quadric in $\PP_3$

2009-10-11

arxiv.org/abs/0910.2053v2

Mathematics

Algebraic Geometry

16pages, Comments welcome

Scientific paper

We investigate the jumping conics of stable vector bundles $E$ of rank 2 on a smooth quadric surface $Q$ with the first Chern class $c_1=\Oo_Q(-1,-1)$ with respect to the ample line bundle $\Oo_Q(1,1)$. We show that the set of jumping conics of $E$ is a hypersurface of degree $c_2(E)-1$ in $\PP_3^*$. 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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