88 research outputs found
On the Gorenstein locus of some punctual Hilbert schemes
Let be an algebraically closed field and let \Hilb_{d}^{G}(\p{N}) be
the open locus of the Hilbert scheme \Hilb_{d}(\p{N}) corresponding to
Gorenstein subschemes. We prove that \Hilb_{d}^{G}(\p{N}) is irreducible for
, we characterize geometrically its singularities for and we
give some results about them when which give some evidence to a
conjecture on the nature of the singular points in \Hilb_{d}^{G}(\p{N}).Comment: The exposition has been improved and some of the main results have
been extended to degree $d\le 9
A structure theorem for 2-stretched Gorenstein algebras
In this paper we study the isomorphism classes of local, Artinian, Gorenstein
k-algebras A whose maximal ideal M satisfies dim_k(M^3/M^4)=1 by means of
Macaulay's inverse system generalizing a recent result by J. Elias and M.E.
Rossi. Then we use such results in order to complete the description of the
singular locus of the Gorenstein locus of the punctual Hilbert scheme of degree
11.Comment: 24 pages. We removed lemma 2.1 because it was false and we modified
the proof of proposition 3.2 accordingly inserting some new due reference
Examples of rank two aCM bundles on smooth quartic surfaces in
Let be a smooth quartic surface and let
. In the
present paper we classify locally free sheaves of rank on
such that , and
for . We also deal with
their stability.Comment: 22 pages. Exposition improve
TDOA--based localization in two dimensions: the bifurcation curve
In this paper, we complete the study of the geometry of the TDOA map that
encodes the noiseless model for the localization of a source from the range
differences between three receivers in a plane, by computing the Cartesian
equation of the bifurcation curve in terms of the positions of the receivers.
From that equation, we can compute its real asymptotic lines. The present
manuscript completes the analysis of [Inverse Problems, Vol. 30, Number 3,
Pages 035004]. Our result is useful to check if a source belongs or is closed
to the bifurcation curve, where the localization in a noisy scenario is
ambiguous.Comment: 11 pages, 3 figures, to appear in Fundamenta Informatica
Canonical curves with low apolarity
Let be an algebraically closed field and let be a non--hyperelliptic
smooth projective curve of genus defined over . Since the canonical
model of is arithmetically Gorenstein, Macaulay's theory of inverse systems
allows to associate to a cubic form in the divided power --algebra
in variables. The apolarity of is the minimal number of
linear form in needed to write as sum of their divided power cubes.
It is easy to see that the apolarity of is at least and P. De Poi
and F. Zucconi classified curves with apolarity when is the complex
field. In this paper, we give a complete, characteristic free, classification
of curves with apolarity (and )
Irreducibility of the Gorenstein loci of Hilbert schemes via ray families
We analyse the Gorenstein locus of the Hilbert scheme of points on
i.e. the open subscheme parameterising zero-dimensional
Gorenstein subschemes of of degree . We give new sufficient
criteria for smoothability and smoothness of points of the Gorenstein locus. In
particular we prove that this locus is irreducible when and find its
components when . The proof is relatively self-contained and it does
not rely on a computer algebra system. As a by--product, we give equations of
the fourth secant variety to the -th Veronese reembedding of
for .Comment: v4: final. v2: expanded proof of Theorems A and B. 33 pages, comments
welcome
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