3,072 research outputs found
On generic identifiability of symmetric tensors of subgeneric rank
No full textWe prove that the general symmetric tensor in of rank
r is identifiable, provided that r is smaller than the generic rank. That is,
its Waring decomposition as a sum of r powers of linear forms is unique. Only
three exceptional cases arise, all of which were known in the literature. Our
original contribution regards the case of cubics (), while for we
rely on known results on weak defectivity by Ballico, Ciliberto, Chiantini, and
Mella.Comment: 20 pages, two M2 files as ancillary files; v2 contains some changes
in section
On the study of decompositions of forms in four variables
No full textIn the space of sextic forms in 4 variables with a decompo-sition of length 18 we determine and describe a closed subvariety which contains all non-identifiable sextics. The description of the subvari-ety is geometric, but one can derive from that an algorithm which can guarantee that a given form is identifiable
On a-adic approximation of the first neighborhood of an ideal
No full textGiven the strict transorm J of a graded ideal I, we determine an approximation
procedure for finding the generators of J from the generators of I
Lectures on the structure of projective embeddings
No full textWe draw a picture of the “status of the art” in the theory of defective varieties, i.e. varieties whose secant spaces fill up a variety of dimension smaller than expected. Some links between the theory of defective varieties and other fields of algebraic geometry and mathematics are outlined. Several open problems and current researches on the subject are presented
Non complete linear series on curves
No full textThe paper is concerned with some properties of linear series on smooth plane curves; in fact, we study mainly the case of cubic curves. The main result describes the growth of the dimension of non complete linear series, generalizing to cubics
a well known result of Gieseker, about linear series on the projective lines
Interpolation in higher codimension
No full textFollowing the suggestions contained in [5], I will discuss constructions that generalizes the interpolation problems for divisors to the case of varieties of higher codimension, with emphasis on the case of curves arising as 0-loci of vector bundles of rank 2 in P3
On some algebraic and geometric extension of the theory of adjoints
No full textWe consider an excellent curve on a regular surface without any assumption on the base field. Our investigation shows that all the classical definitions of adjoints can be given and compared
On form ideals and Artin-Rees conditions
No full textWe look for conditions which make two ideals and in a noetherian ring A have the same form ideal in an associated graded ring GA(a^r). More precisely, when and and fi–f'i lies in a^r m m>t0, forall i , we give a necessary and sufficient condition to have, involving the first syzygies modules both of (f1,...,fn) and (f'1,...,f'n); our proof is based on the Artin-Rees lemma. Finally we show that, when the sequence f1,...,fn is regular and for an integer q, then f1–f'i in a^q+1 forall i implies T*=T'
Obstructions of t'Hooft curves
No full textWe present here a class of curves whose obstructedness depends only on the degree and genus; more precisely, for such curves C there is an explicit arithmetic inequality, involving only the degree and the genus of C, which is satisfied if and only if C is obstructed
p-basi e basi differenziali di un anello
No full textSi definiscono e si paragonano le basi dei moduli differenziali di un anello noetheriano
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