showing 18 related works from this author
Subvarieties of the Grassmannian $G(1,N)$ with small secant variety
2002
Classification of n-dimensional subvarieties of G(1, 2n) that can be projected to G(1, n + 1)
2005
A structure theorem is given for n-dimensional smooth subvarieties of the Grassmannian G(1, N); with N >= n + 3, that can be isomorphically projected to G(1, n + 1). A complete classification in the cases N = 2n + 1 and N = 2n follows, as a corollary.
A conjecture on special linear systems of $mathbb{P}^3$
2005
Projecting 4-folds from G(1, 5) to G(1, 4)
2002
We study 4-dimensional subvarieties of the Grassmannian G(1,5) with singular locus of dimension at most 1 that can be isomorphically projected to G(1,4).
Standard classes on the blow-up of $\mathbb{P}^n$ at points in very general position
2012
On globally generated vector bundles on projective spaces
2009
AbstractA classification is given for globally generated vector bundles E of rank k on Pn having first Chern class c1(E)=2. In particular, we get that they split if k<n unless E is a twisted null-correlation bundle on P3. In view of the well-known correspondence between globally generated vector bundles and maps to Grassmannians, we obtain, as a corollary, a classification of double Veronese embeddings of Pn into a Grassmannian G(k−1,N) of (k−1)-planes in PN.
On a class of special linear systems of P^3
2003
In this paper we deal with linear systems of P^3 through fat points. We consider the behavior of these systems under a cubo-cubic Cremona transformation that allows us to produce a class of special systems which we conjecture to be the only ones.
Quasi-Homogeneous Linear Systems on with Base Points of Multiplicity multiplicity 5
2003
In this paper we consider linear systems of ℙ2 with all but one of the base points of multiplicity 5. We give an explicit way to evaluate the dimensions of such systems
Elementary (-1)-curves of P-3
2006
In this note we deal with rational curves in P^3 which are images of a line by means of a finite sequence of cubo-cubic Cremona transformations. We prove that these curves can always be obtained applying to the line a sequence of such transformations increasing at each step the degree of the curve. As a corollary we get a result about curves that can give speciality for linear systems of P^3.
Blown-up toric surfaces with non-polyhedral effective cone
2020
We construct examples of projective toric surfaces whose blow-up at a general point has a non-polyhedral pseudo-effective cone, both in characteristic $0$ and in every prime characteristic $p$. As a consequence, we prove that the pseudo-effective cone of the Grothendieck-Knudsen moduli space $\overline M_{0,n}$ of stable rational curves is not polyhedral for $n\geq 10$ in characteristic $0$ and in characteristic $p$, for all primes $p$. Many of these toric surfaces are related to a very interesting class of arithmetic threefolds that we call arithmetic elliptic pairs of infinite order. Their analysis in characteristic $p$ relies on tools of arithmetic geometry and Galois representations in …
A counterexample to a conjecture on linear systems on ℙ3
2004
In this paper [1] Ciliberto proposes a conjecture in order to characterize special linear systems of IPn through multiple base points. In this note we give a counterexample to this conjecture by showing that there is a substantial difference between the speciality of linear systems on IP 2 and those of IP3.
On multiples of divisors associated to Veronese embeddings with defective secant variety
2009
In this note we consider multiples aD, where D is a divisor of the blow-up of P^n along points in general position which appears in the Alexander and Hirschowitz list of Veronese embeddings having defective secant varieties. In particular we show that there is such a D with h^1(X,D) > 0 and h^1(X,2D) = 0.
On double Veronese embeddings in the Grassmannian G(1,N)
2004
We classify all the embeddings of P^n in a Grassmannian of lines G(1,N) such that the composition with Pl\"ucker is given by a linear system of quadrics of P^n.
Cox ring of the generic fiber
2017
Abstract Given a surjective morphism π : X → Y of normal varieties satisfying some regularity hypotheses we prove how to recover a Cox ring of the generic fiber of π from the Cox ring of X. As a corollary we show that in some cases it is also possible to recover the Cox ring of a very general fiber, and finally we give an application in the case of the blowing-up of a toric fiber space.
On globally generated vector bundles on projective spaces II
2014
Extending a previous result of the authors, we classify globally generated vector bundles on projective spaces with first Chern class equal to three.
On base loci of higher fundamental forms of toric varieties
2019
We study the base locus of the higher fundamental forms of a projective toric variety $X$ at a general point. More precisely we consider the closure $X$ of the image of a map $({\mathbb C}^*)^k\to {\mathbb P}^n$, sending $t$ to the vector of Laurent monomials with exponents $p_0,\dots,p_n\in {\mathbb Z}^k$. We prove that the $m$-th fundamental form of such an $X$ at a general point has non empty base locus if and only if the points $p_i$ lie on a suitable degree-$m$ affine hypersurface. We then restrict to the case in which the points $p_i$ are all the lattice points of a lattice polytope and we give some applications of the above result. In particular we provide a classification for the se…
On cubic elliptic varieties
2013
Let X->P^(n-1) be an elliptic fibration obtained by resolving the indeterminacy of the projection of a cubic hypersurface Y of P^(n+1) from a line L not contained in Y. We prove that the Mordell-Weil group of the elliptic fibration is finite if and only if the Cox ring of X is finitely generated. We also provide a presentation of the Cox ring of X when it is finitely generated.
Del Pezzo elliptic varieties of degree d <= 4
2019
Let Y be a smooth del Pezzo variety of dimension n>=3, i.e. a smooth complex projective variety endowed with an ample divisor H such that K_Y = (n+1)H. Let d be the degree H^n of Y and assume that d >= 4. Consider a linear subsystem of |H| whose base locus is zero-dimensional of length d. The subsystem defines a rational map onto P^{n-1} and, under some mild extra hypothesis, the general pseudofibers are elliptic curves. We study the elliptic fibration X -> P^{n-1} obtained by resolving the indeterminacy and call the variety X a del Pezzo elliptic variety. Extending the results of [7] we mainly prove that the Mordell-Weil group of the fibration is finite if and only if the Cox ring…