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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 $mathbb{P}^3$ 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 $mathcal{E}$ on three-dimensional rational normal scrolls $S(a_0,a_1,a_2)$. We give a monadic description of $H$-instanton bundles and we prove the existence of $mu$-stable $H$-instanton bundles on $S(a_0,a_1,a_2)$ for any admissible charge $k=c_2(mathcal{E})H$. Then we deal in more detail with $S(a,a,b)$ and $S(a_0,a_1,a_2)$ with $a_0+a_1>a_2$ and even degree. Finally we describe a nice component of the moduli space of $mu$-stable bundles whose points represent $H$-instantons.
We prove that the kernel bundle of the evaluation morphism of global sections, namely the syzygy bundle, of a sufficiently ample line bundle on a smooth projective variety is slope stable with respect to any polarization. This settles a conjecture of Ein-Lazarsfeld-Mustopa.
We classify the Ulrich vector bundles of arbitrary rank on smooth projective varieties of minimal degree. In the process, we prove the stability of the sheaves of relative differentials on rational scrolls.
We study instanton bundles $E$ on $mathbb{P}^1times mathbb{P}^1 times mathbb{P}^1$. We construct two different monads which are the analog of the monads for instanton bundles on $mathbb P^3$ and on the flag threefold $F(0,1,2)$. We characterize the G
We propose a general definition of mathematical instanton bundle with given charge on any Fano threefold extending the classical definitions on $mathbb P^3$ and on Fano threefold with cyclic Picard group. Then we deal with the case of the blow up of
We generalise Flo{}ystads theorem on the existence of monads on the projective space to a larger set of projective varieties. We consider a variety $X$, a line bundle $L$ on $X$, and a base-point-free linear system of sections of $L$ giving a morphis