1,770 research outputs found
Three-by-three bound entanglement with general unextendible product bases
We discuss the subject of Unextendible Product Bases with the orthogonality
condition dropped and we prove that the lowest rank non-separable
positive-partial-transpose states, i.e. states of rank 4 in 3 x 3 systems are
always locally equivalent to a projection onto the orthogonal complement of a
linear subspace spanned by an orthogonal Unextendible Product Basis. The
product vectors in the kernels of the states belong to a non-zero measure
subset of all general Unextendible Product Bases, nevertheless they can always
be locally transformed to the orthogonal form. This fully confirms the
surprising numerical results recently reported by Leinaas et al. Parts of the
paper rely heavily on the use of Bezout's Theorem from algebraic geometry.Comment: 36 page
Numerically flat Higgs vector bundles
After providing a suitable definition of numerical effectiveness for Higgs
bundles, and a related notion of numerical flatness, in this paper we prove,
together with some side results, that all Chern classes of a Higgs-numerically
flat Higgs bundle vanish, and that a Higgs bundle is Higgs-numerically flat if
and only if it is has a filtration whose quotients are flat stable Higgs
bundles. We also study the relation between these numerical properties of Higgs
bundles and (semi)stability.Comment: 11 page
Exploring the biochemistry at the extracellular redox frontier of bacterial mineral Fe(III) respiration
Many species of the bacterial Shewanella genus are notable for their ability to respire in anoxic environments utilizing insoluble minerals of Fe(III) and Mn(IV) as extracellular electron acceptors. In Shewanella oneidensis, the process is dependent on the decahaem electron-transport proteins that lie at the extracellular face of the outer membrane where they can contact the insoluble mineral substrates. These extracellular proteins are charged with electrons provided by an inter-membrane electron-transfer pathway that links the extracellular face of the outer membrane with the inner cytoplasmic membrane and thereby intracellular electron sources. In the present paper, we consider the common structural features of two of these outer-membrane decahaem cytochromes, MtrC and MtrF, and bring this together with biochemical, spectroscopic and voltammetric data to identify common and distinct properties of these prototypical members of different clades of the outer-membrane decahaem cytochrome superfamily
The moduli space of hypersurfaces whose singular locus has high dimension
Let be an algebraically closed field and let and be integers with
and Consider the moduli space of
hypersurfaces in of fixed degree whose singular locus is
at least -dimensional. We prove that for large , has a unique
irreducible component of maximal dimension, consisting of the hypersurfaces
singular along a linear -dimensional subspace of . The proof
will involve a probabilistic counting argument over finite fields.Comment: Final version, including the incorporation of all comments by the
refere
Introduction to derived categories of coherent sheaves
In these notes, an introduction to derived categories and derived functors is
given. The main focus is the bounded derived category of coherent sheaves on a
smooth projective variety.Comment: 24 pages, minor changes, same content as published versio
D-modules on 1|1 Supercurves
It is known that to every 1|1 dimensional supercurve X there is associated a
dual supercurve \hat{X}, and a superdiagonal \Delta in their product. We
establish that the categories of D-modules on X, \hat{X}, and \Delta are
equivalent. This follows from a more general result about D-modules and purely
odd submersions. The equivalences preserve tensor products, and take vector
bundles to vector bundles. Line bundles with connection are studied, and
examples are given where X is a superelliptic curve.Comment: 18 page
Crystal melting on toric surfaces
We study the relationship between the statistical mechanics of crystal
melting and instanton counting in N=4 supersymmetric U(1) gauge theory on toric
surfaces. We argue that, in contrast to their six-dimensional cousins, the two
problems are related but not identical. We develop a vertex formalism for the
crystal partition function, which calculates a generating function for the
dimension 0 and 1 subschemes of the toric surface, and describe the
modifications required to obtain the corresponding gauge theory partition
function.Comment: 30 pages; v2: references adde
Log canonical thresholds of Del Pezzo Surfaces in characteristic p
The global log canonical threshold of each non-singular complex del Pezzo
surface was computed by Cheltsov. The proof used Koll\'ar-Shokurov's
connectedness principle and other results relying on vanishing theorems of
Kodaira type, not known to be true in finite characteristic.
We compute the global log canonical threshold of non-singular del Pezzo
surfaces over an algebraically closed field. We give algebraic proofs of
results previously known only in characteristic . Instead of using of the
connectedness principle we introduce a new technique based on a classification
of curves of low degree. As an application we conclude that non-singular del
Pezzo surfaces in finite characteristic of degree lower or equal than are
K-semistable.Comment: 21 pages. Thorough rewrite following referee's suggestions. To be
published in Manuscripta Mathematic
- …