2020/07/08 by Antonelli, Vincenzo, Malaspina, Francesco · 1 citation
#13C14 #14F05 #14J60 #Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2007.04164
We propose a notion of instanton bundle (called H-instanton bundle) on any projective variety of dimension three polarized by a very ample divisor H, that naturally generalizes the ones on ℙ3 and on the flag threefold F(0,1,2). We discuss the cases of Veronese and Fano threefolds. Then we deal with H-instanton bundles E on three-dimensional rational normal scrolls S(a0,a1,a2). We give a monadic description of H-instanton bundles and we prove the existence of μ-stable H-instanton bundles on S(a0,a1,a2) for any admissible charge k=c2(E)H. Then we deal in more detail with S(a,a,b) and S(a0,a1,a2) with a0+a1>a2 and even degree. Finally we describe a nice component of the moduli space of μ-stable bundles whose points represent H-instantons.