Related papers: H-Instanton Bundles on Three-Dimensional Smooth To…
We prove the rationality and irreducibility of the moduli space of mathematical instanton vector bundles of arbitrary rank and charge on $\mathbb P^3$. In particular, the result applies to the rank-2 case. This problem was first studied by…
We prove that the moduli space of mathematical instanton bundles on ${\Bbb P}^3$ with $c_2=5$ is smooth.
We prove that the space of mathematical instantons with second Chern class 5 over ${\mathbb P}_3$ is smooth and irreducible. Unified and simple proofs for the same statements in case of second Chern class $\leq 4$ are contained.
In this article we study the Gieseker-Maruyama moduli spaces $\mathcal{B}(e,n)$ of stable rank 2 algebraic vector bundles with Chern classes $c_1=e\in\{-1,0\},\ c_2=n\ge1$ on the projective space $\mathbb{P}^3$. We construct two new…
This paper is devoted to the theory of symplectic instanton bundles on an odd dimensional projective space ${\mathbb P}^{2n+1}$ with $n\ge 2$. We study the 't Hooft instanton bundles introduced by Ottaviani and a new family of instanton…
In this paper we establish the existence of monads on special Cartesian products of projective spaces. Special in the sense that we mimick monads on instanton bundles. We construct monads on…
Symplectic instanton vector bundles on the projective space $\mathbb{P}^3$ constitute a natural generalization of mathematical instantons of rank 2. We study the moduli space $I_{n,r}$ of rank-$2r$ symplectic instanton vector bundles on…
Using monads, we construct a large class of stable bundles of rank 2 and 3 on 3-fold hypersurfaces, and study the set of all possible Chern classes of stable vector bundles.
We consider an extension of the instanton bundles definition, given by Casnati-Coskun-Genk-Malaspina, for Fano threefolds, in order to include non locally-free ones on the blow-up $\widetilde{\mathbb{P}^{3}},$ of the projective $3-$space at…
The Hodge Conjecture is equivalent to a statement about conditions under which a complex vector bundle on a smooth complex projective variety admits a holomorphic structure. I advertise a class of abelian four-folds due to Mumford where…
We study some generalized instanton algebras which are required to describe `instantonic complex rank 2 bundles'. The spaces on which the bundles are defined are not prescribed from the beginning but rather are obtained from some natural…
In this paper, using the Atiyah-Ward equivalence and a theorem of Hitchin, one makes to correspond to certain bundles on the projective space, which are extensions of instanton bundles (in particular, these new bundles may have the first…
In this paper, we study Ulrich bundles on smooth toric threefolds with Picard number$~2$, namely $\mathbb P(\mathcal O_{\mathbb P^{2}}(a_0) \oplus \mathcal O_{\mathbb P^{2}}(a_1))$. We construct resolutions and monads for Ulrich bundles of…
Motivated by gauge theory on manifolds with exceptional holonomy, we construct examples of stable bundles on K3 surfaces that are invariant under two involutions: one is holomorphic; and the other is anti-holomorphic. These bundles are…
In this paper we establish the existence of monads on Cartesian products of projective spaces. We construct vector bundles associated to monads on…
Instantons, emerged in particle physics, have been intensely studied since the 1970's and had an enormous impact in mathematics since then. In this paper, we focus on one particular way in which mathematical physics has guided the…
In this paper we construct indecomposable vector bundles associated to monads on Cartesian products of odd dimension projective spaces. Specifically we establish the existence of monads on…
In this work we study the moduli spaces of instanton bundles on the flag twistor space $F:=F(0,1,2)$. We stratify them in terms of the minimal twist supporting global sections and we introduce the notion of (special) 't Hooft bundle on $F$.…
We present a new family of monads whose cohomology is a stable rank two vector bundle on $\mathbb{P}^3$. We also study the irreducibility and smoothness together with a geometrical description of some of these families. These facts are used…
Mathematical instanton bundles of rank 4 and $c_2=2$ on ${\mathbb P}^4$ have a smoothquasiprojective moduli space, which is shown via a direct GIT construction. A complete classification of jumping lines of these vector bundles is obtained.…