相关论文: Rank two bundles on P^n with isolated cohomology

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…

In this article we prove a general result on a nef vector bundle $E$ on a projective manifold $X$ of dimension $n$ depending on the vector space $H^{n,n} (X, E). $ It is also shown that $H^{n,n} (X, E)=0$ for an indecomposable nef rank 2…

We consider principal bundles over homogeneous spaces G/P, where P is a parabolic subgroup of a semisimple and simply connected complex linear algebraic group G. We prove that a holomorphic principal H--bundle, where H is a complex…

We study sheaves E on a smooth projective curve X which are minimal with respect to the property that $h^0(E \otimes L) >0$ for all line bundles L of degree zero. We show that these sheaves define ample divisors D(E) on the Picard torus…

Let E be a stable rank two normalized vector bundle on P3. If H is a general plane we show that h^0(E_H(1)) \leq 2+c_1. It follows that h^0(E(1)) \leq 2+c_1.

We propose a three-step program for the classification of stable rank 2 bundles on the projective space $\mathbb{P}^3$ inspired by an article by Hartshorne and Rao. While this classification program has been successfully completed for…

We study certain moduli spaces of stable vector bundles of rank two on cubic and quartic threefolds. In many cases under consideration, it turns out that the moduli space is complete and irreducible and a general member has vanishing…

A finite length graded $R$-module $M$ has the Weak Lefschetz Property if there is a linear element $\ell$ in $R$ such that the multiplication map $\times\ell: M_i\to M_{i+1}$ has maximal rank. The set of linear forms with this property form…

Let $X$ be a complex surface obtained as the quotient of the complex Euclidean space $\mathbb{C}^2$ by a discrete subgroup of rank $3$. We investigate the cohomology group $H_0^1(X, E)$ with compact support for a unitary flat line bundle…

Mathematical instanton bundles on $ P_3$ have their analogues in rank--$2n$ instanton bundles on odd dimensional projective spaces $ P_{2n+1}$. The families of special instanton bundles on these spaces generalize the special 'tHooft bundles…

We study the problem of rationality of an infinite series of components, the so-called Ein components, of the Gieseker-Maruyama moduli space $M(e,n)$ of rank 2 stable vector bundles with the first Chern class $e=0$ or -1 and all possible…

In this work we deal with vector bundles of rank two on a Fano manifold $X$ with $b_2=b_4=1$. We study the nef and pseudoeffective cones of the corresponding projectivizations and how these cones are related to the decomposability of the…

We consider the moduli space of rank two, odd degree, semi-stable Real vector bundles over a real curve, calculating the singular cohomology ring in odd and zero characteristic for most examples.

We improve Ottaviani's splitting criterion for vector bundles on a quadric hypersurface and obtain the equivalent of the result by Rao, Mohan Kumar and Peterson. Then we give the classification of rank 2 bundles without "inner" cohomology…

We give a cohomological classification of vector bundles of rank $2$ on a smooth affine threefold over an algebraically closed field having characteristic unequal to $2$. As a consequence we deduce that cancellation holds for rank $2$…

There is a long-standing conjecture which states that every uniform algebraic vector bundle of rank $r<2n$ on the $n$-dimensional projective space $\mathbb{P}^n$ over an algebraically closed field of characteristic $0$ is homogeneous. This…

We demonstrate the existence of a uniform and nonhomogeneous vector bundle $E$ of rank $(n-d)(m+1)-1$ over Grassmannian $\mathbb{G}(d,n)$, where $m>d$ and $1\le d \le n-d-1$ with a $\mathbb{P}$-homogeneity degree $h(E)=d$. Particularly, we…

Let $X$ be a Fano threefold with index $i_X$ and fundamental line bundle $\mathcal O_X(h)$. We classify $\mu$-semistable rank two bundles $\mathcal E$ on $X$ with $c_1(\mathcal E)=0$, $h^0(\mathcal E) \ne 0$ and $h^1(\mathcal…

In this paper, we use characteristic classes of the canonical vector bundles and the Poincar\' {e} dualality to study the structure of the real homology and cohomology groups of oriented Grassmann manifold $G(k, n)$. Show that for $k=2$ or…

We study in this paper a new family of stable algebraic symplectic vector bundles of rank $ 2n $ on the complex projective space $P^{2n+1}$ whose classical null correlation bundles belongs. We show that these bundles are invariant under a…