1,442 research outputs found
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
The determination of integral closures and geometric applications
We express explicitly the integral closures of some ring extensions; this is
done for all Bring-Jerrard extensions of any degree as well as for all general
extensions of degree < 6; so far such an explicit expression is known only for
degree < 4 extensions. As a geometric application we present explicitly the
structure sheaf of every Bring-Jerrard covering space in terms of coefficients
of the equation defining the covering; in particular, we show that a degree-3
morphism f : Y --> X is quasi-etale if and only if the first Chern class of the
sheaf f_*(O_Y) is trivial (details in Theorem 5.3). We also try to get a
geometric Galoisness criterion for an arbitrary degree-n finite morphism; this
is successfully done when n = 3 and less satifactorily done when n = 5.Comment: Advances in Mathematics, to appear (no changes, just add this info
A sufficient condition for a number to be the order of a nonsingular derivation of a Lie algebra
A study of the set N_p of positive integers which occur as orders of
nonsingular derivations of finite-dimensional non-nilpotent Lie algebras of
characteristic p>0 was initiated by Shalev and continued by the present author.
The main goal of this paper is to show the abundance of elements of N_p. Our
main result shows that any divisor n of q-1, where q is a power of p, such that
, belongs to N_p. This extends its special
case for p=2 which was proved in a previous paper by a different method.Comment: 10 pages. This version has been revised according to a referee's
suggestions. The additions include a discussion of the (lower) density of the
set N_p, and the results of more extensive machine computations. Note that
the title has also changed. To appear in Israel J. Mat
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
Ample filters and Frobenius amplitude
Let be a projective scheme over a field. We show that the vanishing
cohomology of any sequence of coherent sheaves is closely related to vanishing
under pullbacks by the Frobenius morphism. We also compare various definitions
of ample locally free sheaf and show that the vanishing given by the Frobenius
morphism is, in a certain sense, the strongest possible. Our work can be viewed
as various generalizations of the Serre Vanishing Theorem.Comment: 15 pages, major improvement in results, typo fixed in Equation 2.5,
warning footnote added to Lemma 2.
Noncommutative ampleness for multiple divisors
The twisted homogeneous coordinate ring is one of the basic constructions of
the noncommutative projective geometry of Artin, Van den Bergh, and others.
Chan generalized this construction to the multi-homogeneous case, using a
concept of right ampleness for a finite collection of invertible sheaves and
automorphisms of a projective scheme. From this he derives that certain
multi-homogeneous rings, such as tensor products of twisted homogeneous
coordinate rings, are right noetherian. We show that right and left ampleness
are equivalent and that there is a simple criterion for such ampleness. Thus we
find under natural hypotheses that multi-homogeneous coordinate rings are
noetherian and have integer GK-dimension.Comment: 11 pages, LaTeX, minor corrections, to appear in J. Algebr
Derived categories of cubic fourfolds
We discuss the structure of the derived category of coherent sheaves on cubic
fourfolds of three types: Pfaffian cubics, cubics containing a plane and
singular cubics, and discuss its relation to the rationality of these cubics.Comment: 18 page
Albert algebras over curves of genus zero and one
Albert algebras and other Jordan algebras are constructed over curves of
genus zero and one, using a generalization of the Tits process and the first
Tits construction due to Achhammer.Comment: 37 page
Frobenius Splittings
We give a gentle introduction to Frobenius splittings. Then we recall a few
results that have been obtained with the method.Comment: 21 pages, typos correcte
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