Articoli su riviste
- Secants of Lagrangian Grassmannians,con Jarek Buczynski, in corso di pubblicazione su Annali di Matematica Pura ed Applicata, arXiv.
Abstract:
We study the
dimensions of secant varieties of the Grassmannian of Lagrangian
subspaces in a symplectic vector space. We calculate these dimensions
for third
and fourth secant varieties. Our result is obtained by providing a
normal form
for four general points on such a Grassmannian and by explicitly
calculating
the tangent spaces at these four points.
- Sections of homogeneous vector bundles, Journal of Algebra 323 (2010) 2301–2317, arXiv.
Abstract:
In this work we
give a method for computing sections of homogeneous vector
bundles on any rational homogeneous variety G/P of type ADE. Our main
tool is
the equivalence of categories between homogeneous vector bundles on G/P
and
finite dimensional representations of a given quiver with relations.
Our result
generalizes the work of Ottaviani and Rubei Quivers and the cohomology of
homogeneous
vector bundles, Duke Math. 2006.
- Effective results on Picard bundles via M-regularity, con Francesco Prantil, Le Matematiche 43,1 (2008) 181–203, link.
Abstract:
In this paper we
study some properties, namely Global Generation and Strong Normal
Presentation, of specific types of (twists of) Picard bundles over the
Jacobian of a curve. Our main tool is the notion of M-regularity
introduced by G. Pareschi and M.Popa.
- The Horrocks-Mumford bundle restricted to planes, Collectanea Mathematica 58,1 (2007) 101–117, arXiv.
Abstract:
We study the
behavior of the Horrocks-Mumford bundle when restricted to a
plane P^2 in P^4, looking for all possible minimal free resolutions for
the
restricted bundle. To each of the 6 resolutions (4 stable and 2
unstable) we
find, we then associate a subvariety of the Grassmannian G(2,4) of
planes in
P^4. We thus obtain a filtration of the Grassmannian, which we describe
in the
second part of this work.
Articoli su atti di convegni (refereed)
- On simplicity and stability of tangent bundles of rational homogeneous varieties, Proceedings of the 2008 Grenoble Summer School “Geometric Methods in Representation Theory”, (Séminaires et Congrès de la Société Mathématique de France), to appear, HAL open archive.
Abstract:
Given a rational
homogeneous variety G/P where G is complex simple and of
type ADE, we prove that the tangent bundles T(G/P) is simple, meaning
that its only endomorphisms are scalar multiples of the identity. This
result
combined with Hitchin-Kobayashi correspondence implies stability of th
tangent bundle with respect to the anticanonical polarization. Our main
tool
is the equivalence of categories between homogeneous vector bundles on
G/P and
finite dimensional representations of a given quiver with relations.
Preprints
- A note on secants of Grassmannians, Quaderno Matematico n.613 (June 2011), Università degli Studi di Trieste, link.
Abstract:
Let G(k,n) be the Grassmannian of k-subspaces in an n-dimensional
complex vector space, k \ge 3. For a projective variety X, let
sigma_s(X) denote its s-secant variety, namely the closure of the union
of linear spans of all the s-tuples of independent points lying on X.
We classify all defective sigma_s(G(k,n)), for s \le 12.
Manoscritti in preparazione
- A quiver version of the BGG resolution, in preparazione.
- Moduli spaces of orthogonal bundles, in preparazione.