167 research outputs found
On a Poisson structure on the space of Stokes matrices
In this paper we study the map associating to a linear differential operator
with rational coefficients its monodromy data. The operator has one regular and
one irregular singularity of Poincare' rank 1. We compute the Poisson structure
of the corresponding Monodromy Preserving Deformation Equations on the space of
the monodromy data.Comment: 16 pages,Tex,to be published in IMR
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
A conjecture on special linear systems of P^3
In this note we consider the behavior of linear systems of P^3 through fat
points under a cubo-cubic Cremona transformation. This allows us to produce a
class of special systems which we conjecture to be the only ones.Comment: 4 pages, LaTe
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
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