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Francesco Malaspina

Publications and source records attributed to Francesco Malaspina.

44 records · Page 3Linked to original sources
arXiv2009

Low Rank Vector Bundles on the Grassmannian G(1,4)

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 notion of $L$-regularity in order to prove a splitting criterion for rank 2 vector bundles with only a finite number of vanishing conditions. In the second part we give the classification of rank 2 and rank 3 vector bundles without "inner" cohomology (i.e. $H^i_*(E)=H^i(E\otimes\Q)=0$ for any $i=2,3,4$) on G(1,4) by studying the associated monads.

math.AG↗
arXiv2009

Cohomological Characterization of Vector Bundles on Grassmannians of Lines

We introduce a notion of regularity for coherent sheaves on Grassmannians of lines. We use this notion to prove some extension of Evans-Griffith criterion to characterize direct sums of line bundles. We also give a cohomological characterization of exterior and symmetric powers of the universal bundles of the Grassmannian.

math.AG↗
arXiv2008

A splitting criterion for vector bundles on blowing ups of the plane

Let $f_s: X_s \to {\bf {P}}^2$ be the blowing-up of $s$ distinct points and $E$ a vector bundle on $X_s$. Here we give a cohomological criterio which is equivalent to $E \cong f_s^\ast (A)$ with $A$ a direct sum of line bundles. We also some cohomological characterizations of very particular rank 2 vector bundles on ${\bf {P}}^2$.

math.AG↗
arXiv2008

Vector Bundles on Products of Varieties with $n$-blocks Collections

Here we consider the product of varieties with $n$-blocks collections . We give some cohomological splitting conditions for rank 2 bundles. A cohomological characterization for vector bundles is also provided. The tools are Beilinson's type spectral sequences generalized by Costa and Miró-Roig. Moreover we introduce a notion of Castelnuovo-Mumford regularity on a product of finitely many projective spaces and smooth quadric hypersurfaces in order to prove two splitting criteria for vector bundle with arbitrary rank.

math.AG↗
arXiv2008

The Equations of Singular Loci of Ample Divisors on (Subvarieties of) Abelian Varieties

In this paper we consider ideal sheaves associated to the singular loci of a divisor in a linear system $|L|$ of an ample line bundle on a complex abelian variety. We prove an effective result on their (continuous) global generation, after suitable twists by powers of $L$. Moreover we show that similar results hold for subvarieties of a complex abelian variety.

math.AG↗
arXiv2008

A Few Splitting Criteria for Vector Bundles

We prove a few splitting criteria for vector bundles on a quadric hypersurface and Grassmannians. We give also some cohomological splitting conditions for rank 2 bundles on multiprojective spaces. The tools are monads and a Beilinson's type spectral sequence generalized by Costa and Miró-Roig.

math.AG↗
arXiv2008

Qregularity and an Extension of Evans-Griffiths Criterion to Vector Bundles on Quadrics

Here we define the concept of Qregularity for coherent sheaves on quadrics. In this setting we prove analogs of some classical properties. We compare the Qregularity of coherent sheaves on $\Q_n\subset \mathbb P^{n+1}$ with the Castelnuovo-Mumford regularity of their extension by zero in $\mathbb P^{n+1}$. We also classify the coherent sheaves with Qregularity $-\infty$. We use our notion of Qregularity in order to prove an extension of Evans-Griffiths criterion to vector bundles on Quadrics. In particular we get a new and simple proof of the Knörrer's characterization of ACM bundles.

math.AG↗