1,720,977 research outputs found
Ample bodies and Terracini loci of projective varieties
No full textWe introduce the notion of ample body of a projective variety and use it to prove emptiness results for Terracini loci and specific identifiability results for toric and homogeneous varieties
On base loci of higher fundamental forms of toric varieties
Full text linkWe 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 (C*)k→Pn, sending t to the vector of Laurent monomials with exponents p0,...,pn∈Zk. 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 pi lie on a suitable degree-m affine hypersurface. We then restrict to the case in which the points pi 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 second fundamental forms on toric surfaces, and we also give some new examples of weighted 3-dimensional projective spaces whose blowing up at a general point is not Mori dream
On a class of special linear systems of P3
No full textIn this paper we deal with linear systems of P3 through fat points. We consider the behavior of these systems under a cubic Cremona transformation that allows us to produce a class of special systems which we conjecture to be the only one
Cox ring of the generic fiber
Full text linkGiven 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
A counterexample to a conjecture on linear systems on IP3
No full textIn 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 secant defectiveness and identifiability of Segre-Veronese varieties
No full textWe give an almost asymptotically sharp bound for the non secant defectiveness and identifiability of Segre-Veronese varieties. We also provide new examples of defective Segre-Veronese varieties
On Mori chamber and stable base locus decompositions
No full textThe effective cone of a Mori dream space admits two wall-and-chamber decompositions called Mori chamber and stable base locus decompositions. In general the former is a nontrivial refinement of the latter. We investigate, from both the geometrical and combinatorial viewpoints, the differences between these decompositions. Furthermore, we provide a criterion to establish whether the two decompositions coincide for a Mori dream space of Picard rank two, and we construct an explicit example of a Mori dream space of Picard rank two for which the decompositions are different, showing that our criterion is sharp. Finally, we classify the smooth toric 3-folds of Picard rank three for which the two decompositions are different
- …
