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
a brief survey written by request for
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
and Dror Varolin. To appear in Duke Math Journal.
Core versus graded core and global sections of line bundles
Eero Hyry. To appear in Transactions of AMS.
On a non-vanishing conjecture of Kawamata and the core of an ideal
Eero Hyry. American Journal of Math. Volume 125. 2003.
Uniform approximation of Abhyankar valuation ideals in smooth function fields,
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,
Behavior of the test ideal under smooth and etale homomorphisms,
Journal of Algebra,
Uniform Behavior of Symbolic Powers of Ideals, with
Lawrence Ein and
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 F-regular 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 20-th annual
Japanese commutative algebra conference.)
On the commutation of the test ideal under localization and completion,
Gennady Lyubeznik. Transactions of AMS
A Tight closure proof of Fujita's freeness conjecture for very ample
line bundles Mathematische Annalen
Rational and non-rational Algebraic Varieties: Lectures
of János Kollár.
This is a detailed write up of
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 F-regularity are equivalent in graded rings,
Gennady Lyubeznik. American Journal of Mathematics, 1999
F-regularity deforms for Q-Gorenstein 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,
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
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) 35-53.
Tight Closure and the Kodaira Vanishing Theorem,
Journal fur die riene und angewandte Mathematics, 484 (1997)
Linear Growth of Primary Decompositions of Monomial Ideals
Irena Swanson, Communications in Algebra, 25(10), 3071-3079
Simplicity of Rings of Differential Operators in Prime Characteristic
Michel Van den Bergh,
Proc. London Math. Society, (3) 75 (1997) 32-62.
The D-module structure of F-split rings,
Mathematical Research Letters, 2 377-386 (1995)
A Tight Closure Approach to Arithmetic Macaulayfication
Illinois Journal of Math.
40, 310-329 (1996)
F-Rational Rings have Rational Singularities,
American Journal, 119, 159-180 (1997)
- Tight Closure of Parameter Ideals,
115, 41-60, (1994)
- Test ideals in local rings, Transactions AMS
- Singularities of certain ladder determinantal varieties, with Donna
Glassbrenner, Journal of Pure and Applied Algebra, 101, 59-75 (1995).
- Tight Closure and Graded Integral Extensions, Journal of Algebra,
175, 568-574, (1995)