Related papers: A splitting criterion for rank 2 vector bundles on…

This paper treats the strict semi-stability of the symmetric powers $S^k E$ of a stable vector bundle $E$ of rank $2$ with even degree on a smooth projective curve $C$ of genus $g \geq 2$. The strict semi-stability of $S^2 E$ is equivalent…

Let $X_0$ be an irreducible smooth projective curve defined over $\overline{\mathbb Q}$ and $f_0 : X_0 \rightarrow \mathbb{P}^1_{\overline{\mathbb Q}}$ a nonconstant morphism whose branch locus is contained in the subset $\{0,1, \infty\}…

A $k$-very ample line bundle L on a Del Pezzo Surface is numerically characterized. We find that the set of the exceptional curves and effective divisors with selfintersection zero, $\cal S$, plays a very important rule in checking the…

We consider mixed integer linear programs where free integer variables are expressed in terms of nonnegative continuous variables. When this model only has two integer variables, Dey and Louveaux characterized the intersection cuts that…

Let $X$ be a connected, smooth, and projective curve of genus $g$ over an algebraically closed field of characteristic $p >0$. This paper investigates a characteristic-$p$ analogue of a well-known fact concerning flat vector bundles in…

This paper gives a new elementary proof of the theorem that all vector bundles on $\mathbb P^1$ split into the direct sum of line bundles. The proof is based on the study of divisors associated to germs of sections at the generic point.

Here we define the concept of $L$-regularity for coherent sheaves on the Grassmannian G(1,4) as a generalization of Castelnuovo-Mumford regularity on ${\bf{P}^n}$. In this setting we prove analogs of some classical properties. We use our…

Developing a previous idea of Faltings, we characterize the complete intersections of codimension 2 in P^n, n>=3, over an algebraically closed field of any characteristic, among l.c.i. X, as those that are subcanonical and…

We show that a proper algebraic n-dimensional scheme Y admits nontrivial vector bundles of rank n, even if Y is non-projective, provided that there is a modification containing a projective Cartier divisor that intersects the exceptional…

Let H be a complex Lie group acting holomorphically on a complex analytic space X such that the restriction to X_{\mathrm{red}} of every H-invariant regular function on X is constant. We prove that an H-equivariant holomorphic vector bundle…

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…

According to the Grothendieck-Lefschetz theorem from SGA 2, there are no nontrivial line bundles on the punctured spectrum $U_R$ of a local ring $R$ that is a complete intersection of dimension $\ge 4$. Dao conjectured a generalization for…

The moduli space $M(c_2)$, of stable rank two vector bundles of degree one on a very general quintic surface $X\subset {\mathbb P}^3$, is irreducible for all $c_2\geq 4$ and empty otherwise.

A line bundle L on a smooth curve X is nonspecial if and only if L admits a presentation L=K_X -D +E for some effective divisors D and E>0 on X with gcd (D, E)=0 and h^0 (X, O_X (D))=1. In this work, we define a minimal presentation of L…

We consider all complex projective manifolds X that satisfy at least one of the following three conditions: 1. There exists a pair $(C ,\varphi)$, where $C$ is a compact connected Riemann surface and $\varphi : C\to X$ a holomorphic map,…

Let E and F be vector bundles over a complex projective smooth curve X, and suppose that 0 -> E -> W -> F -> 0 is a nontrivial extension. Let G be a subbundle of F, and D an effective divisor on X. We give a criterion for the subsheaf G(-D)…

The classification of algebraic vector bundles of rank 2 over smooth affine fourfolds is a notoriously difficult problem. Isomorphism classes of such vector bundles are not uniquely determined by their Chern classes, in contrast to the…

We study the positivity of the first Chern class of a rank r Ulrich vector bundle E on a smooth n-dimensional variety $X \subseteq \mathbb P^N$. We prove that $c_1(E)$ is very positive on every subvariety not contained in the union of lines…

It is easy to imagine that a subvariety of a vector bundle, whose intersection with every fibre is a vector subspace of constant dimension, must necessarily be a sub-bundle. We give two examples to show that this is not true, and several…

The concurrence vectors are proposed by employing the fundamental representation of $A_n$ Lie algebra, which provides a clear criterion to evaluate the entanglement of bipartite system of arbitrary dimension for both pure and mixed states.…