Compactification of the moduli space of minimal instantons on the Fano threefold $V_4$

Abstract

We study semi-stable sheaves of rank $2$ with Chern class $c_1=0$, $c_2=2$ and $c_3=0$ on the Fano 3-folds $V_4$ of Picard number $1$, degree $4$ and index $2$. We show the moduli space of such sheaves is isomorphic to the moduli space of semi-stable rank $2$ even degree vector bundles on a genus $2$ curve. This provides a natural smooth compatification of the moduli space of Ulrich bundles of rank $2$ on $V_4$.

18 pages. Changed title. Final version, to appear in European Journal of Mathematics. arXiv admin note: text overlap with arXiv:1810.04737

References in corpus (4)

• Instanton bundles on Fano threefolds
• Instanton bundles on the blow up of the projective $3$-space at a point
• Singular locus of instanton sheaves on ${\mathbb{P}}^3$
• Compactification of the moduli space of instanton sheaves on the Fano threefold $V_5$