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Search Results: 1 - 10 of 74339 matches for " Maria Lucia Fania "
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Fano manifolds as ample divisors
Maria Lucia Fania
Le Matematiche , 1999,
Abstract: We study polarized manifolds (X, L) with L having a smooth element A in its linear system which is a Fano manifold of coindex 3 and second Betti number greater or equal than 2.
Skew-symmetric matrices and Palatini scrolls
Daniele Faenzi,Maria Lucia Fania
Mathematics , 2009,
Abstract: We prove that, for m greater than 3 and k greater than m-2, the Grassmannian of m-dimensional subspaces of the space of skew-symmetric forms over a vector space of dimension 2k is birational to the Hilbert scheme of Palatini scrolls in P^(2k-1). For m=3 and k greater than 3, this Grassmannian is proved to be birational to the set of pairs (E,Y), where Y is a smooth plane curve of degree k and E is a stable rank-2 bundle on Y whose determinant is O(k-1).
Vector spaces of skew-symmetric matrices of constant rank
Maria Lucia Fania,Emilia Mezzetti
Mathematics , 2010,
Abstract: We study the orbits of vector spaces of skew-symmetric matrices of constant rank 2r and type (N+1)x(N+1) under the natural action of SL(N+1), over an algebraically closed field of characteristic zero. We give a complete description of the orbits for vector spaces of dimension 2, relating them to some 1-generic matrices of linear forms. We also show that, for each rank two vector bundle on P^2 defining a triple Veronese embedding of P^2 in G(1,7), there exists a vector space of 8 x 8 skew-symmetric matrices of constant rank 6 whose kernel bundle is the dual of the given rank two vector bundle.
On the Hilbert scheme of varieties defined by maximal minors
Daniele Faenzi,Maria Lucia Fania
Mathematics , 2010,
Abstract: We compute the dimension of the Hilbert scheme of subvarieties of positive dimension in projective space which are cut by maximal minors of a matrix with polynomial entries.
On the Hilbert scheme of Palatini threefolds
Maria Lucia Fania,Emilia Mezzetti
Mathematics , 2002,
Abstract: We study the Hilbert scheme of Palatini threefolds X in P^5. We prove that such a scheme has an irreducible component containing X which is birational to the Grassmannian G(3,14) and we determine the exceptional locus of the birational map.
Hilbert schemes of some threefold scrolls over F_e
Maria Lucia Fania,Flaminio Flamini
Mathematics , 2014,
Abstract: Hilbert schemes of suitable smooth, projective 3-fold scrolls over the Hirzebruch surface F_e, with e > 1, are studied. An irreducible component of the Hilbert scheme parametrizing such varieties is shown to be generically smooth of the expected dimension and the general point of such a component is described. This article generalizes the study of Hilbert schemes done in arXiv:1110.5464 for e=1.
The dimension of the Hilbert scheme of special threefolds
GianMario Besana,Maria Lucia Fania
Mathematics , 2004,
Abstract: The Hilbert scheme of projective 3-folds of codimension 3 or more that are linear scrolls over the projective plane or over a smooth quadric surface or that are quadric or cubic fibrations over the projective line is studied. All known such threefolds of degree from 7 to 11 are shown to correspond to smooth points of an irreducible component of their Hilbert scheme, whose dimension is computed. A relationship with the locus of good determinantal subschemes is investigated
Hilbert scheme of some threefold scrolls over the Hirzebruch surface F_1
Gian Mario Besana,Maria Lucia Fania,Flaminio Flamini
Mathematics , 2011,
Abstract: Hilbert schemes of suitable smooth, projective manifolds of low degree which are 3-fold scrolls over the Hirzebruch surface F_1 are studied. An irreducible component of the Hilbert scheme parametrizing such varieties is shown to be generically smooth of the expected dimension and the general point of such a component is described.
On families of rank-2 uniform bundles on Hirzebruch surfaces and Hilbert schemes of their scrolls
Gian Mario Besana,Maria Lucia Fania,Flaminio Flamini
Mathematics , 2015,
Abstract: Several families of rank-two vector bundles on Hirzebruch surfaces are shown to consist of all very ample, uniform bundles. Under suitable numerical assumptions, the projectivization of these bundles, embedded by their tautological line bundles as linear scrolls, are shown to correspond to smooth points of components of their Hilbert scheme, the latter having the expected dimension. If e=0,1 the scrolls fill up the entire component of the Hilbert scheme, while for e=2 the scrolls exhaust a subvariety of codimension 1.
Boundedness for codimension two submanifolds of quadrics
Lucia Fania,Giorgio Ottaviani
Mathematics , 1997,
Abstract: Arrondo, Sols and De Cataldo proved that there are only finitely many families of codimension two subvarieties not of general type in the smooth quadric of dimension $n+2$ for $n\ge 2 $, $n\neq 4$. In this paper we drop the assumption $n\neq 4$ from the previous result (obviously the assumption $n\ge 2$ cannot be removed).
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