Some recent preprints of Karen E. Smith
You can also visit some of my collaborators' homepages by clicking on
their underlined names in the below list.

The jet schemes of a monomial scheme with
Russell Goward.

Motivic Integration,
a brief survey written by request for
MSRI's
Concepts page. A slightly longer version of the survey
was written for MSRI's Emissary newsletter, and appeared in the
2003 issue .

Jumping coefficients of multiplier ideals
with
Lawrence Ein,
Rob Lazarsfeld
and Dror Varolin. To appear in Duke Math Journal.

Core versus graded core and global sections of line bundles
with
Eero Hyry. To appear in Transactions of AMS.

On a nonvanishing conjecture of Kawamata and the core of an ideal
with
Eero Hyry. American Journal of Math. Volume 125. 2003.

Uniform approximation of Abhyankar valuation ideals in smooth function fields,
with
Lawrence Ein and
Rob Lazarsfeld, American Journal of Math, 2003.

The Hodge Conjecture.
This is an expository paper in Archimedes 2002, the
journal of the Finnish Math and Physical Society.
The figures are not included in this version.

Tight closure and vanishing theorems.
(Lecture notes from summer school called "Vanishing theorems and effective
results in algebraic geometry", 2001)
electronically published by the Intenational Center for Theoretical Physics,
Trieste Italy.

Behavior of the test ideal under smooth and etale homomorphisms,
with
Ana Bravo,
Journal of Algebra,

Uniform Behavior of Symbolic Powers of Ideals, with
Lawrence Ein and
Rob Lazarsfeld,
Inventiones Math, 2001

An algebraic proof of Zak's inequality for
the dimension of the Gauss image
with Aron Simis and Bernd Ulrich, Math Z.

The strong test ideal with Nobuo Hara, Illinois Journal of Math.

Globally Fregular varieties: applications to vanishing theorems for
quotients of Fano varieties,
2000 Fulton Volume of the Michigan Journal of Math.

The multiplier ideal is a universal test ideal
Hartshorne volume of Communications in Algebra (2000)

An introduction to tight closure.
A survey in the proceedings of the Messina Conference on
Commutative Algebra and Algebrais Geometry.
(Note: this is essentially the same as the paper earlier listed here as
notes from the 20th annual
Japanese commutative algebra conference.)

On the commutation of the test ideal under localization and completion,
with
Gennady Lyubeznik. Transactions of AMS

A Tight closure proof of Fujita's freeness conjecture for very ample
line bundles Mathematische Annalen

Rational and nonrational Algebraic Varieties: Lectures
of János Kollár.
This is a detailed write up of
János Kollár's,
Course At the EMS summer
school in Algebraic Geometry in Eger, Hungary, August 1996.
Also available in the
Duke Archives paper number 9707013. We plan to eventually
turn this into a book.

Weak and Strong Fregularity are equivalent in graded rings,
with
Gennady Lyubeznik. American Journal of Mathematics, 1999

Fregularity deforms for QGorenstein rings,
Just a brief note proving the above statement in characteristic zero
(essentially just pointing out that Kollár has already proved this).

Tight Closure commutes with localization in binomial rings
Proceedings of AMS

Sparse Systems of Parameters for Determinantal Varieties,
with Donna Glassbrenner, Advances in Applied Mathematics 19,
529558 (1997)

Fujita's Freeness Conjecture in terms of Local Cohomology
Journal of Algebraic Geometry,

Vanishing Theorems, Singularities, and Effective Bounds in Algebraic
Geometry Via Prime Characteristic Local Algebra
to appear in Proc. Symposia of Pure Mathematics, eds J. Kollár
and R. Lazarsfeld. An expositional article
surveying of applications of new ideas in characteristic
p commutative
algebra to algebraic geometry. Includes several new results as well.
Important: Be sure to also download this
Erratum as well.

Tight Closure in Graded Rings,
Kyoto Journal of Mathematics, Vol 37 No. 1. (1997) 3553.

Tight Closure and the Kodaira Vanishing Theorem,
with
Craig Huneke,
Journal fur die riene und angewandte Mathematics, 484 (1997)

Linear Growth of Primary Decompositions of Monomial Ideals
with
Irena Swanson, Communications in Algebra, 25(10), 30713079
(1997)

Simplicity of Rings of Differential Operators in Prime Characteristic
with
Michel Van den Bergh,
Proc. London Math. Society, (3) 75 (1997) 3262.

The Dmodule structure of Fsplit rings,
Mathematical Research Letters, 2 377386 (1995)

A Tight Closure Approach to Arithmetic Macaulayfication
with
Ian Aberbach
and
Craig Huneke,
Illinois Journal of Math.
40, 310329 (1996)

FRational Rings have Rational Singularities,
American Journal, 119, 159180 (1997)
 Tight Closure of Parameter Ideals,
Inventiones Math.
115, 4160, (1994)
 Test ideals in local rings, Transactions AMS
 Singularities of certain ladder determinantal varieties, with Donna
Glassbrenner, Journal of Pure and Applied Algebra, 101, 5975 (1995).
 Tight Closure and Graded Integral Extensions, Journal of Algebra,
175, 568574, (1995)