Related papers: Simplicity of generic Steiner bundles

We prove abundance for a minimal Kaehler threefold which is not both simple and non-Kummer. Recall that a variety is simple if there is no compact subvariety of positive dimension through a sufficiently general point . Furthermore we prove…

In this paper, we show that the cohomology of a general stable bundle on a Hirzebruch surface is determined by the Euler characteristic provided that the first Chern class satisfies necessary intersection conditions. More generally, we…

When the cohomology ring of a generalized Bott manifold with $\mathbb{Q}$-coefficient is isomorphic to that of a product of complex projective spaces $\mathbb{C}P^{n_i}$, the generalized Bott manifold is said to be $\mathbb{Q}$-trivial. We…

For each pair $(e,\sigma)$ of integers satisfying $2e+3\sigma\ge 0$, $\sigma\leq -2$, and $e+\sigma\equiv 0\pmod{4}$, with four exceptions, we construct a minimal, simply connected symplectic 4-manifold with Euler characteristic $e$ and…

In this paper we show that on a general sextic hypersurface $X\subset \bf P^4$, a rank 2 vector bundle $E$ splits if and only if $h^1(E(n))=0$ for any $n \in \bf Z$. We get thus a characterization of complete intersection curves in $X$

We study simply-laced simple affine Lie algebra bundles over complex surfaces X. Given any Kodaira curve C in X, we construct such a bundle over X. After deformations, it becomes trivial on every irreducible component of C provided that…

We show that a normalized rank two vector bundle, E, on P2 splits if and only if h1(E(-1)) = 0. Using this fact we give another proof of a theorem of Chiantini and Valabrega. Finally we describe the normalized bundles with h1(E(-1)) <= 4.

Given a finite simplicial complex L and a collection of pairs of spaces indexed by its vertex set, one can define their polyhedral product. We record a simple formula for its Euler characteristic. In special cases the formula simplifies…

Let A be a regular domain of dimension d containing an infinite field and let n be an integer with 2n\geq d+3. For a stably free A-module P of rank n, we prove that (i) P has a unimodular element if and only if the euler class of P is zero…

Let $G$ be a complex connected reductive algebraic group that acts on a smooth complex algebraic variety $X$, and let $E$ be a $G$-equivariant algebraic vector bundle over $X$. A section of $E$ is regular if it is transversal to the zero…

We formulate an equivariant conservation of number, which proves that a generalized Euler number of a complex equivariant vector bundle can be computed as a sum of local indices of an arbitrary section. This involves an expansion of the…

Let G be a simple simply-connected group scheme over a regular local scheme U. Let E be a principal G-bundle over A^1_U trivial away from a subscheme finite over U. We show that E is not necessarily trivial and give some criteria of…

We prove that the minimal Euler characteristic of a closed symplectic four-manifold with given fundamental group is often much larger than the minimal Euler characteristic of almost complex closed four-manifolds with the same fundamental…

This paper concerns obstruction flatness of hypersurfaces $\Sigma$ that arise as unit sphere bundles $S(E)$ of Griffiths negative Hermitian vector bundles $(E, h)$ over K\"ahler manifolds $(M, g).$ We prove that if the curvature of $(E, h)$…

Let Q be a finite quiver without oriented cycles. Denote by U --> M the fine moduli space of stable thin sincere representations of Q with respect to the canonical stability notion. We prove Ext^i(U,U) = 0 for all i >0 and compute the…

In this work we study $k$-type uniform Steiner bundles, being $k$ the lowest degree of the splitting. We prove sharp upper and lower bounds for the rank in the case $k=1$ and moreover we give families of examples for every allowed possible…

In this paper we obtain the following results: (1) Any compact Stein surface with boundary embeds naturally into a symplectic Lefschetz fibration over the 2-sphere. (2) There exists a minimal elliptic fibration over the 2-disk, which is not…

We prove that a general $n$-fold quadric bundle $\mathcal{Q}^{n-1}\rightarrow\mathbb{P}^{1}$, over a number field, with $(-K_{\mathcal{Q}^{n-1}})^n > 0$ and discriminant of odd degree $\delta_{\mathcal{Q}^{n-1}}$ is unirational, and that…

In this paper we characterize minimal free resolutions of homogeneous bundles on P^2. Besides we study stability and simplicity of homogeneous bundles on P^2 by means of their minimal free resolutions; in particular we give a criterion to…

For a line bundle L on a smooth surface S, it is now known that the degree of the Severi variety of cogenus-d curves is given by a universal polynomial in the Chern classes of L and S if L is d-very ample. For S rational, we relax the…