Weakly defective varieties
- L. Chiantini, C. Ciliberto
- Mathematics
- 13 July 2001
A projective variety X is k-weakly defective' when its intersection with a general (k + 1)-tangent hyperplane has no isolated singularities at the k + 1 points of tangency. If X is k-defective, i.e.…
Degenerations of Planar Linear Systems
- C. Ciliberto, R. Miranda
- Mathematics, Computer Science
- 21 February 1997
An approach is proposed based on an analysis of the corresponding linear system on a degeneration of the plane itself, leading to a simple recursion for these dimensions, obtaining results in the ``quasi-homogeneous'' case when all the multiplicities are equal except one.
Projective degenerations of K3 surfaces, Gaussian maps, and Fano threefolds
- C. Ciliberto, A. Lopez, R. Miranda
- Mathematics
- 9 November 1993
SummaryIn this article we exhibit certain projective degenerations of smoothK3 surfaces of degree 2g−2 in ℙg (whose Picard group is generated by the hyperplane class), to a union of two rational…
Homaloidal hypersurfaces and hypersurfaces with vanishing Hessian
- C. Ciliberto, F. Russo, A. Simis
- Mathematics
- 21 January 2007
Geometric Aspects of Polynomial Interpolation in More Variables and of Waring’s Problem
- C. Ciliberto
- Mathematics, Philosophy
- 2001
In this paper I treat the problem of determining the dimension of the vector space of homogeneous polynomials in a given number of variables vanishing with some of their derivatives at a finite set…
The genus of projective curves
- L. Chiantini, C. Ciliberto, V. Gennaro
- Biology
- 1 May 1993
Pencils of minimal degree on curves on a K3 surface.
- G. Pareschi, C. Ciliberto
- Mathematics
- 1995
The gonality of a smooth irreducible projective curve C is the minimal degree of a (necessarily base point free and complete) g\ on C. The main object of this note is the following problem: given a…
On the Concept of k‐Secant Order of a Variety
- L. Chiantini, C. Ciliberto
- Mathematics
- 1 April 2006
For a variety X of dimension n in\sPr, r ⩾ n(k + 1) + k, the kth secant order of X is the number μk(X) of (k + 1)‐secant k‐spaces passing through a general point of the kth secant variety. We show…
ON THE CLASSIFICATION OF IRREGULAR SURFACES OF GENERAL TYPE WITH NONBIRATIONAL BICANONICAL MAP
- F. Catanese, C. Ciliberto, M. M. Lopes
- Mathematics
- 1998
The present paper is devoted to the classification of irregular surfaces of general type with pg > 3 and nonbirational bicanonical map. Our main result is that, if S is such a surface and if S is…
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