5,559 research outputs found
A small and non-simple geometric transition
Following notation introduced in the recent paper \cite{Rdef}, this paper is
aimed to present in detail an example of a "small" geometric transition which
is not a "simple" one i.e. a deformation of a conifold transition. This is
realized by means of a detailed analysis of the Kuranishi space of a Namikawa
cuspidal fiber product, which in particular improves the conclusion of
Y.~Namikawa in Remark 2.8 and Example 1.11 of \cite{N}. The physical interest
of this example is presenting a geometric transition which can't be immediately
explained as a massive black hole condensation to a massless one, as described
by A.~Strominger \cite{Strominger95}.Comment: 22 pages. v2: final version to appear in Mathematical Physics,
Analysis and Geometry. Minor changes: title, abstract, result in Remark 3
emphasized by Theorem 5, as suggested by a referee. Some typos correcte
Embedding non-projective Mori Dream Spaces
This paper is devoted to extend some Hu-Keel results on Mori dream spaces
(MDS) beyond the projective setup. Namely, \Q-factorial algebraic varieties
with finitely generated class group and Cox ring, here called \emph{weak} Mori
dream spaces (wMDS), are considered. Conditions guaranteeing the existence of a
neat embedding of a (completion of a) wMDS into a complete toric variety are
studied, showing that, on the one hand, those which are complete and admitting
low Picard number are always projective, hence Mori dream spaces in the sense
of Hu-Keel. On the other hand, an example of a wMDS does not admitting any neat
embedded \emph{sharp} completion (i.e. Picard number preserving) into a
complete toric variety is given, on the contrary of what Hu and Keel exhibited
for a MDS. Moreover, termination of the Mori minimal model program (MMP) for
every divisor and a classification of rational contractions for a complete wMDS
are studied, obtaining analogous conclusions as for a MDS. Finally, we give a
characterization of a wMDS arising from a small \Q-factorial modification of
a projective weak \Q-Fano variety.Comment: v4: Final version accepted for pubblication in Geometriae Dedicata.
Minor changes. Adopting the Journal TeX-macros changed the statements'
enumeration. 46 pages, 3 figure
Rate-Distortion Classification for Self-Tuning IoT Networks
Many future wireless sensor networks and the Internet of Things are expected
to follow a software defined paradigm, where protocol parameters and behaviors
will be dynamically tuned as a function of the signal statistics. New protocols
will be then injected as a software as certain events occur. For instance, new
data compressors could be (re)programmed on-the-fly as the monitored signal
type or its statistical properties change. We consider a lossy compression
scenario, where the application tolerates some distortion of the gathered
signal in return for improved energy efficiency. To reap the full benefits of
this paradigm, we discuss an automatic sensor profiling approach where the
signal class, and in particular the corresponding rate-distortion curve, is
automatically assessed using machine learning tools (namely, support vector
machines and neural networks). We show that this curve can be reliably
estimated on-the-fly through the computation of a small number (from ten to
twenty) of statistical features on time windows of a few hundreds samples
Z-linear Gale duality and poly weighted spaces (PWS)
The present paper is devoted to discussing Gale duality from the Z-linear
algebraic point of view. This allows us to isolate the class of Q-factorial
complete toric varieties whose class group is torsion free, here called poly
weighted spaces (PWS), as an interesting generalization of weighted projective
spaces (WPS).Comment: 29 pages: revised version to appear in Linear Algebra and Its
Applications. Major changes: the paper has been largely rewritten following
refree's comments. In particular, main geometric results have been
anticipated giving rise to the motivational Section
A --factorial complete toric variety with Picard number 2 is projective
This paper is devoted to settle two still open problems, connected with the
existence of ample and nef divisors on a Q-factorial complete toric variety.
The first problem is about the existence of ample divisors when the Picard
number is 2: we give a positive answer to this question, by studying the
secondary fan by means of Z-linear Gale duality. The second problem is about
the minimum value of the Picard number allowing the vanishing of the Nef cone:
we present a 3-dimensional example showing that this value cannot be greater
then 3, which, under the previous result, is also the minimum value
guaranteeing the existence of non-projective examples.Comment: 10 pages, 5 figures. Minor changes following the referee's advise:
list of notation suppressed, few typos fixed, references updated. Final
version to appear in Advances in Geometr
A Q-factorial complete toric variety is a quotient of a poly weighted space
We prove that every Q-factorial complete toric variety is a finite quotient
of a poly weighted space (PWS), as defined in our previous work
arXiv:1501.05244. This generalizes the Batyrev-Cox and Conrads description of a
Q-factorial complete toric variety of Picard number 1, as a finite quotient of
a weighted projective space (WPS) \cite[Lemma~2.11]{BC} and
\cite[Prop.~4.7]{Conrads}, to every possible Picard number, by replacing the
covering WPS with a PWS. As a consequence we describe the bases of the subgroup
of Cartier divisors inside the free group of Weil divisors and the bases of the
Picard subgroup inside the class group, respectively, generalizing to every
Q-factorial complete toric variety the description given in arXiv:1501.05244,
Thm. 2.9, for a PWS.Comment: 25+9 pp. Post-final version of our paper published in
Ann.Mat.Pur.Appl.(2017),196,325-347: after its publication we realized that
Prop.~3.1 contains an error strongly influencing the rest of the paper. Here
is a correct revision (first 25 pp.: this version will not be published) and
the Erratum appearing soon in Ann. Mat. Pur. Appl. (last 9 pp.) correcting
only those parts affected by the erro
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