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Dive into the research topics where Maria Lucia Fania is active.

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Featured researches published by Maria Lucia Fania.


Communications in Algebra | 2005

THE DIMENSION OF THE HILBERT SCHEME OF SPECIAL THREEFOLDS

Gian Mario Besana; Maria Lucia Fania

The Hilbert scheme of 3-folds in ℙ n , n ≥ 6 , that are scrolls over ℙ 2 or over a smooth quadric surface Q ⊂ ℙ 3 or that are quadric or cubic fibrations over ℙ 1 is studied. All known such threefolds of degree 7 ≤ d ≤ 11 are shown to correspond to smooth points of an irreducible component of their Hilbert scheme, whose dimension is computed.


Advances in Geometry | 2016

Hilbert schemes of some threefold scrolls over F_e

Maria Lucia Fania; Flaminio Flamini

Abstract Hilbert schemes of suitable smooth, projective threefold scrolls over the Hirzebruch surface 𝔽e, e ≥ 2, 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.


International Journal of Mathematics | 2006

Evidence to subcanonicity of codimension two subvarieties of G(1,4)

Enrique Arrondo Esteban; Maria Lucia Fania

In this paper, we show that any smooth subvariety of codimension two in G(1,4) (the Grassmannian of lines of P-4) of degree at most 25 is subcanonical. Analogously, we prove that smooth subvarieties of codimension two in G(1,4) that are not of general type have degree <= 32 and we classify all of them. In both classifications, any subvariety in the final list is either a complete intersection or the zero locus of a section of a twist of the rank-two universal bundle on G(1,4).


arXiv: Algebraic Geometry | 2015

On families of rank-2 uniform bundles on Hirzebruch surfaces and Hilbert schemes of their scrolls

Gian Mario Besana; Maria Lucia Fania; Flaminio Flamini

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 ll up the entire component of the Hilbert scheme, while for e = 2 the scrolls exhaust a subvariety of codimension 1:


Manuscripta Mathematica | 1993

When K+(n-4)L fails to be nef

Maria Lucia Fania

Let X be a smooth complex projective variety of dimension n and let L be an ample line bundle on X. We study polarized pairs (X,L) for which K+(n−3)L is nef but K+(n−4)L fails to be nef.


Transactions of the American Mathematical Society | 1991

Polarized surfaces of Δ-genus 3

Maria Lucia Fania; Elvira Laura Livorni

Let X be a smooth, complex, algebraic, projective surface and let 2 0 L be an ample line bundle on it. Let A = A(Z, L) = cx(L) +2-h (L) denote the A-genus of the pair (X, L). The purpose of this paper is to classify such pairs under the assumption that A = 3 and the complete linear system \L\ contains a smooth curve. If d > 7 and g > A, Fujita has shown that L is very ample and g = A. If d > 7 and g A there are still open cases to solve in which completely different methods are needed.


Advances in Geometry | 2002

On the Hilbert scheme of Palatini threefolds

Maria Lucia Fania; Emilia Mezzetti


Mathematische Nachrichten | 1997

Degree Ten Manifolds of Dimension n Greater than or Equal to 3

Maria Lucia Fania; Elvira Laura Livorni


Mathematische Nachrichten | 2006

Degree Nine Manifolds of Dimension Greater than or Equal to 3

Maria Lucia Fania; Elvira Laura Livorni


Mathematische Annalen | 2010

Skew-symmetric matrices and Palatini scrolls

Daniele Faenzi; Maria Lucia Fania

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