Abstract:
We construct some infinite series of families of stable rank 2 vector bundles on the projective space $\mathbb P^3$ with odd first Chern class $c_1=-1$ and arbitrary second Chern class $c_2=2n$ with $n\ge2$. They are distinct from the series of families of bundles which were constructed by Hartshorne in 1978. We conjecture that for $n\ge3$ these families lie in the irreducible components of the moduli space of stable bundles distinct from the components that include Hartshorne's families. In this article we prove the conjecture for $n=3$. In this case the scheme of moduli of stable rank 2 vector bundles with $c_1=-1$ and $c_2=6$ on $\mathbb P^3$ has at least two irreducible components.
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