896 research outputs found
Multiplier Ideals and Modules on Toric Varieties
A simple formula computing the multiplier ideal of a monomial ideal on an
arbitrary affine toric variety is given. Variants for the multiplier module and
test ideals are also treated.Comment: 8 pages, to appear in Mathematische Zeitschrif
The D-Module structure of R[F]-modules
Let R be a regular ring essentially of finite type over a perfect field k. An
R-module M is called a unit R[F]-module if it comes equipped with an
isomorphism F*M-->M where F denotes the Frobenius map on Spec R, and F* is the
associated pullback functor. It is well known that M then carries a natural
D-module structure. In this paper we investigate the relation between the unit
R[F]-structure and the induced D-structure on M. In particular, it is shown
that, if k is algebraically closed and M is a simple finitely generated unit
R[F]-module, then it is also simple as a D-module. An example showing the
necessity of k being algebraically closed is also given.Comment: 25 pages. Some minor changes following referee's suggestion. To
appear in Trans. AM
The intersection homology D-module in finite characteristic
For Y a closed normal subvariety of codimension c of a smooth complex variety
X, Brylinski and Kashiwara showed that the local cohomology module H^c_Y(X,O_X)
contains a unique simple D_X-submodule, denoted by L(Y,X). In this paper the
analogous result is shown for X and Y defined over a perfect field of finite
characteristic. Moreover, a local construction of Ll(Y,X) is given, relating it
to the theory of tight closure. From the construction one obtains a criterion
for the D_X-simplicity of H^c_Y(X).Comment: 23 pages, streamlined exposition according to referee's suggestion
An informal introduction to multiplier ideals
Multiplier ideals, and the vanishing theorems they satisfy, have found many
applications in recent years. In the global setting they have been used to
study pluricanonical and other linear series on a projective variety. More
recently, they have led to the discovery of some surprising uniform results in
local algebra.
The present notes aim to provide a gentle introduction to the
algebraically-oriented local side of the theory. They follow closely a short
course on multiplier ideals given in September 2002 at the Introductory
Workshop of the program in commutative algebra at MSRI.Comment: 28 pages, 5 figures, minor corrections and improvements according to
editors suggestion
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