809 research outputs found
Local syzygies of multiplier ideals
In recent years, multiplier ideals have found many applications in local and
global algebraic geometry. Because of their importance, there has been some
interest in the question of which ideals on a smooth complex variety can be
realized as multiplier ideals. Other than integral closure no local
obstructions have been known up to now, and in dimension two it was established
by Favre-Jonsson and Lipman-Watanabe that any integrally closed ideal is
locally a multiplier ideal. We prove the somewhat unexpected result that
multiplier ideals in fact satisfy some rather strong algebraic properties
involving higher syzygies. It follows that in dimensions three and higher,
multiplier ideals are very special among all integrally closed ideals.Comment: 8 page
On codimension two flats in Fermat-type arrangements
In the present note we study certain arrangements of codimension flats in
projective spaces, we call them "Fermat arrangements". We describe algebraic
properties of their defining ideals. In particular, we show that they provide
counterexamples to an expected containment relation between ordinary and
symbolic powers of homogeneous ideals.Comment: 9 page
A Frobenius variant of Seshadri constants
We define and study a version of Seshadri constant for ample line bundles in
positive characteristic. We prove that lower bounds for this constant imply the
global generation or very ampleness of the corresponding adjoint line bundle.
As a consequence, we deduce that the criterion for global generation and very
ampleness of adjoint line bundles in terms of usual Seshadri constants holds
also in positive characteristic.Comment: 16 page
Waldschmidt constants for Stanley-Reisner ideals of a class of graphs
In the present note we study Waldschmidt constants of Stanley-Reisner ideals
of a hypergraph and a graph with vertices forming a bipyramid over a planar
n-gon. The case of the hypergraph has been studied by Bocci and Franci. We
reprove their main result. The case of the graph is new. Interestingly, both
cases provide series of ideals with Waldschmidt constants descending to 1. It
would be interesting to known if there are bounded ascending sequences of
Waldschmidt constants.Comment: 7 pages, 2 figure
Learning and predicting time series by neural networks
Artificial neural networks which are trained on a time series are supposed to
achieve two abilities: firstly to predict the series many time steps ahead and
secondly to learn the rule which has produced the series. It is shown that
prediction and learning are not necessarily related to each other. Chaotic
sequences can be learned but not predicted while quasiperiodic sequences can be
well predicted but not learned.Comment: 5 page
On the classification of OADP varieties
The main purpose of this paper is to show that OADP varieties stand at an
important crossroad of various main streets in different disciplines like
projective geometry, birational geometry and algebra. This is a good reason for
studying and classifying them. Main specific results are: (a) the
classification of all OADP surfaces (regardless to their smoothness); (b) the
classification of a relevant class of normal OADP varieties of any dimension,
which includes interesting examples like lagrangian grassmannians. Following
[PR], the equivalence of the classification in (b) with the one of
quadro-quadric Cremona transformations and of complex, unitary, cubic Jordan
algebras are explained.Comment: 13 pages. Dedicated to Fabrizio Catanese on the occasion of his 60th
birthday. To appear in a special issue of Science in China Series A:
Mathematic
Learning and generation of long-range correlated sequences
We study the capability to learn and to generate long-range, power-law
correlated sequences by a fully connected asymmetric network. The focus is set
on the ability of neural networks to extract statistical features from a
sequence. We demonstrate that the average power-law behavior is learnable,
namely, the sequence generated by the trained network obeys the same
statistical behavior. The interplay between a correlated weight matrix and the
sequence generated by such a network is explored. A weight matrix with a
power-law correlation function along the vertical direction, gives rise to a
sequence with a similar statistical behavior.Comment: 5 pages, 3 figures, accepted for publication in Physical Review
Secure and linear cryptosystems using error-correcting codes
A public-key cryptosystem, digital signature and authentication procedures
based on a Gallager-type parity-check error-correcting code are presented. The
complexity of the encryption and the decryption processes scale linearly with
the size of the plaintext Alice sends to Bob. The public-key is pre-corrupted
by Bob, whereas a private-noise added by Alice to a given fraction of the
ciphertext of each encrypted plaintext serves to increase the secure channel
and is the cornerstone for digital signatures and authentication. Various
scenarios are discussed including the possible actions of the opponent Oscar as
an eavesdropper or as a disruptor
Un-Haunting From the Ghost We Killed: IS Research and Education in the Post-Industrial Economy
The field of management emerged in response to the challenges of the industrial age that is now coming to an end. Since its inception, the information systems (IS) research community has argued that the information technology will bring fundamental challenges to the forces that underpin the way we organize our work. The IS discipline played a significant role in bringing the end of the industrial age, fulfilling its early promises. However, the IS community is struggling to find a way to move beyond the powerful institutional and intellectual hegemony based on the industrial-age organization. The proposed panel will take up this challenge and debate several ways of going beyond the hegemony of industrial age organization that has dominated both research and education of the field
Multigraded Castelnuovo-Mumford Regularity
We develop a multigraded variant of Castelnuovo-Mumford regularity. Motivated
by toric geometry, we work with modules over a polynomial ring graded by a
finitely generated abelian group. As in the standard graded case, our
definition of multigraded regularity involves the vanishing of graded
components of local cohomology. We establish the key properties of regularity:
its connection with the minimal generators of a module and its behavior in
exact sequences. For an ideal sheaf on a simplicial toric variety X, we prove
that its multigraded regularity bounds the equations that cut out the
associated subvariety. We also provide a criterion for testing if an ample line
bundle on X gives a projectively normal embedding.Comment: 30 pages, 5 figure
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