Publications and Work in Progress
1. Rees Algebras of Conormal Modules Journal of Pure and Applied Algebra, 193 (2004) 231--249.
We deal with classes of prime ideals whose associated
graded ring is isomorphic to the Rees algebra of the conormal
module. With such prime ideals we describe the divisor class
groups of the associated graded rings. Furthermore we study the
relationship between the normality of the conormal module and the
completeness of components of the associated graded ring.
2. Integrally Closed Modules and their Divisors (with S. Noh and W. Vasconcelos),
Communications in Algebra 33(2005) 4719--4733.
There is a beautiful theory of integrally closed ideals in
regular local rings of dimension two, due to Zariski, several
aspects of which were later extended to modules. Our goal is to
study integral closures of modules over normal domains by attaching
divisors/determinantal ideals to them. They will be of two kinds:
the ordinary Fitting ideal and its divisor, and another
`determinantal'
ideal obtained through Noether normalization. They are useful to
describe the integral closures of some class of modules and to
study the completeness of the modules of K\"ahler differentials.
3. Simple valuation ideals of order 2 in two-dimensional regular local rings (with H. Lee and S. Noh),
Communications of Korean Mathematical society 20(3)(2005) 427--436.
4. Normalization of Modules (with B. Ulrich and W. Vasconcelos), J. Algebra 303(2006) 133--145.
We introduce techniques to derive estimates for the degrees of the
generators of the integral closure of several classes of Rees
algebras of modules, and to bound the length of normalization
processes. In the case of regular base rings, the bounds are
expressed in terms of Buchsbaum--Rim multiplicities and a module
version of Brian\c{c}on--Skoda numbers.
5. Rees algebras of conormal modules. Ph.D. thesis, Rutgers University, 2003.
6. Contracted ideals in regular local rings. (with H. Lee, S. Noh, and D. Rush), Preprint.
7. Specialization and integral closure (with B. Ulrich), Preprint.
8. On the equations of almost complete intersections and birationality. (with A. Simis and W. Vasconcelos), In preparation.
9. The structure of the core of modules. (with L. Fouli), In preparation.
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