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Simone Marchesi

Publications and source records attributed to Simone Marchesi.

28 records · Page 2Linked to original sources
arXiv2016

Branes in the moduli space of framed instantons

In the physicist's language, a brane in a hyperkahler manifold is a submanifold which is either complex or lagrangian with respect to three Kahler structures of the ambient manifold. By considering the fixed loci of certain involutions, we describe branes in Nakajima quiver varieties of all possible types. We then focus on the moduli space of framed torsion free sheaves on the projective plane, showing how the involutions considered act on sheaves, and proving the existence of branes in some cases.

math.AG↗
arXiv2015

Curves with Canonical Models on Scrolls

Let $C$ be an integral and projective curve whose canonical model $C'$ lies on a rational normal scroll $S$ of dimension $n$. We mainly study some properties on $C$, such as gonality and the kind of singularities, in the case where $n=2$ and $C$ is non-Gorenstein, and in the case where $n=3$, the scroll $S$ is smooth, and $C'$ is a local complete intersection inside $S$. We also prove that a rational monomial curve with just one singular point lies on a surface scroll if and only if its gonality is at most $3$, and that it lies on a threefold scroll if and only if its gonality is at most $4$.

math.AG↗
arXiv2014

p-Buchsbaum rank 2 bundles on the projective space

It has been proved by various authors that a normalized, 1-Buchsbaum rank 2 vector bundle on P3 is a nullcorrelation bundle, while a normalized, 2-Buchsbaum rank 2 vector bundle on P3 is an instanton bundle of charge 2. We find that the same is not true for 3-Buchsbaum rank 2 vector bundles on P3, and propose a conjecture regarding the classification of such objects.

math.AG↗
arXiv2014

Moduli of autodual instanton bundles

We provide a description of the moduli space of framed autodual instanton bundles on projective space, focusing on the particular cases of symplectic and orthogonal instantons. Our description will use the generalized ADHM equations which define framed instanton sheaves.

math.AG↗
arXiv2013

Schwarzenberger bundles on smooth projective varieties

We define Schwarzenberger bundles on any smooth projective variety X. We introduce the notions of jumping pairs of a Steiner bundle E on X and determine a bound for the dimension of its jumping locus. We completely classify Steiner bundles whose set of jumping pairs have maximal dimension, proving that they are all Schwarzenberger bundles.

math.AG↗
arXiv2012

Jumping pairs of Steiner bundles

In this work we introduce the definition of Schwarzenberger bundle on a Grassmannian. Recalling the notion of Steiner bundle, we generalize the concept of jumping pair for a Steiner bundle on a Grassmannian. After studying the jumping locus variety and bounding its dimension, we give a complete classification of Steiner bundle with jumping locus of maximal dimension, which all are Schwarzenberger bundles.

math.AG↗
arXiv2011

Covered by Lines and Conic Connected Varieties

We study some properties of an embedded variety covered by lines and give a numerical criterion ensuring the existence of a singular conic through two of its general points. We show that our criterion is sharp. Conic-connected, covered by lines, QEL, LQEL, prime Fano, defective, and dual defective varieties are closely related. We study some relations between the above mentioned classes of objects using celebrated results by Ein and Zak.

math.AG↗
arXiv2011

Varieties Connected by Chains of Lines

In this paper we give for any integer l > 2 a numerical criterion ensuring the existence of a chain of length l of lines through two general points of an irreducible variety X in P^N, involving the degrees and the number of homogeneous polynomials defining X. We show that our criterion is sharp.

math.AG↗
arXiv2009

On the non-existence of orthogonal instanton bundles on P^(2N+1)

In this paper we prove that there do not exist orthogonal instanton bundles on P^(2n+1) . In order to demonstrate this fact, we propose a new way of representing the invariant, introduced by L. Costa and G. Ottaviani, related to a rank 2n instanton bundle on P^(2n+1) .

math.AG↗