New Series of Components of the Moduli Space of Stable Rank 2 Vector Bundles on Projective Space

In this work we study the Gieseker——Maruyama moduli spaces $\mathcal{B}(e,n)$ of stable algebraic vector bundles of rank 2 with Chern classes $c_1=e\in\{-1,0\},\ c_2=n\ge1$ on projective space $\mathbb{P}^3$. We construct two new infinite series $\Sigma_0$ and $\Sigma_1$ of irreducible components of spaces $\mathcal{B}(e,n)$ for $e=0$ and $e=-1$, respectively. The general bundles from these components are constructed as cohomological sheaves of monads, the middle term of which is a symplectic instanton bundle of rank 4 in case $e=0$, a twisted symplectiv bundle in case $e=-1$, respectively. We prove that the series $\Sigma_0$ contains components for all big enough values of $n$ (more precisely, at least for all $n\ge 146$). $\Sigma_0$ gives the next example after instanton components of an infinite family of components of $\mathcal{B}(0,n)$ with this property.