113 research outputs found
On multiples of divisors associated to Veronese embeddings with defective secant variety
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.Comment: 10 pages, LaTe
Elementary (-1)-curves of P^3
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.Comment: 12 pages, LaTe
Cox ring of the generic fiber
Given a surjective morphism of normal varieties satisfying
some regularity hypotheses we prove how to recover a Cox ring of the generic
fiber of from the Cox ring of . 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
A counterexample to a conjecture on linear systems on P^3
In this note we give a counterexample to a conjecture proposed by Ciliberto
about special linear systems of P^n through multiple base points.Comment: 6 pages, LaTe
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