
9441425
On the classification of double meanders of
Mcurves of degree 5.
By Anatoly B. Korchagin*, korchag@math.ttu.edu.
A meander of a plane real projective nonsingular curve of degree
n is its connected component having n real points of
intersection with a line.
Only the oneside component of a nonsingular curve of odd degree can be a
meander. Let a_{1}, a_{2}, ... , a_{n} and
b_{1}, b_{2}, ... , b_{n} be 2n
distinct points of intersection of two lines L_{a} and
L_{b}, respectively, with a component A of a curve of
degree n. An orientation of the component
A defines a cyclic sequence of these 2n points in A.
If, after proper renumbering (if it is necessary), the cyclic sequence is
a_{1}, a_{2}, ... , a_{n}, b_{1},
b_{2}, ... , b_{n} then the component A is
called a double meander with respect to the lines L_{a}
and L_{b}. We consider the isotopy
classification of unions of two lines and an Mcurve of degree
5 having a double meander with respect to the two lines.


94413140
On systems of binomials in toric varieties.
By Shalom Eliahou and
Rafael H Villarreal*, vila@esfm.ipn.mx.
Let k be any field and the toric set
in the affine space A_{k}^{n} given parametrically
by x_{i}=t_{1}^{d1i} ...
t_{m}^{dmi},
1 i n, where D =
(d_{ij}) is an m x n
matrix with nonzero columns and whose entries d_{ij} are
non negative integers.
Given a set of binomials g_{1}, ...,g_{r} in the toric
ideal P of k[], we give a criterion
to decide when rad(g_{1}, ...,g_{r}) = P
and show that this criterion is effective for m=1. This extends to
arbitrary dimension, and to arbitrary fields, an earlier result
which held only for monomial curves over an algebraically
closed field of characteristic zero.


94413151
On residually S_{2} ideals.
By Claudia Polini* and Alberto Corso,
polini@math.hope.
This talk is about cancellation theorems for special ideals in a
local Gorenstein ring R. In its simplest form any such theorem says
that if I, J and L are Rideals such that
LI JI then L
J. Using the so called determinant trick, in general one can only conclude
that L JI : I ,
where denotes the integral closure of
J.
To say that cancellation holds for every such ideal L is equivalent
to say that the R/Jmodule I/JI is faithful, that is to say
JI : I = J. More generally, one can ask for which positive integers
t the equality JI^{t} : I^{t} = J holds.
This kind of question is particularly interesting when the ideal J is a
reduction of the ideal I, that is I^{r+1} =
JI^{r} for some positive integer r. Hence I
JI^{r} : I^{r}. Thus, conditions
of the kind JI^{t} : I^{t} = J, with J a
reduction of I, give a severe bound on the reduction number of
ideals which admit proper reductions.
Our main result, which estends work of C. Huneke, answers the above
questions in the case of ideals satisfying local bounds on the
minimal number of generators and some other residual
properties.


94413159
Depth for complexes, and intersection theorems.
By Srikanth Iyengar*, iyengar@math.missouri.edu.
A new notion of depth for complexes is introduced; this agrees with the
classical definition for modules and coincides with earlier extensions
to complexes, whenever they are defined. Two "AuslanderBuchsbaum" type
theorems are established and using these we give a quick proof of an
extension of the Improved New Intersection Theorem (this uses Hochster's
big CohenMacaulay modules), and also a generalization of the "depth
formula" for tensor products of modules.


94413180
Noether normalizations of some subrings of
graphs.
By Adriàn Alcàntar*, adrian@esfm.ipn.mx.
Let G be a graph on the vertex set V={x_{1}, ...,
x_{n}} and R=k[x_{1}, ...,x_{n}]
a polynomial ring over a field k. The monomial subring or
edge subring of Gis the
ksubalgebra k[G] R generated by the set
of monomials x_{i}x_{j} such that
x_{i} is adjacent to x_{j}.
In this report we study (standard) Noether normalizations of
k[G]. If G is the complete graph on n vertices
we present two explicit Noether are normalizations of k[G],
it will turn out that those normalizations can serve
as a model to find Noether normalizations of k[G] for some
specific graphs.


94416201
Serre's Multiplicity Conjectures for Connected
Algebras.
By Izuru Mori*, mori@math.uta.edu.
Let $R$ be a noetherian regular local commutative ring and $M,N$ be finitely
generated $R$modules. If $\ell (M\otimes _RN)<\infty$, then Serre defined
the intersection multiplicity of $M$ and $N$ by
$$\chi (M,N):=\sum _{i=0}^{\infty}(1)^i\text{length}\Tor ^R_i(M,N).$$
Serre's multiplicity conjectures are:
\bigskip {\bf Conjecture} (Serre, 1961)
Suppose $\el (M\otimes _RN)<\infty$. Then
\begin{itemize}
\item{} (Dimension) $\Kdim M+\Kdim N\leq \Kdim R$.
\item{} (Vanishing) If $\Kdim M+\Kdim N< \Kdim R$, then $\chi (M,N)=0$.
\item{} (Positivity) If $\Kdim M+\Kdim N=\Kdim R$, then $\chi (M,N)>0$.
\end{itemize}
In this talk, we will prove Serre's multiplicity conjectures for (1)
connected algebras (not necessarily commutative) and (2) quantum projective
spaces (which are noncommutative analogues of the commutative projective
spaces), using the intersection multiplicity defined by $\Ext$ groups
instead of $\Tor$ groups. Since these two
definitions of intersection multiplicity agree for commutative conneted
algebras, the first result is a noncommutative generalization of the result
of Peskine and Szpiro. The second result is a generalization of
B\'ezout's Theorem.


94413206
Generalized Auslander Regular Algebras.
By Roberto MartìnezVilla*,
mvilla@matem.unam.mx.


94413248
Noetherian domains inside a homomorphic image of a
completion II.
By Heinzer William, Christel Rotthaus* and Sylvia Wiega rotthaus@math.msu.edu.


94413259
Associated graded rings of normal ideals.
By Sam Huckaba and Thomas Marley*,
tmarley@mathstat.unl.edu.
We show how to use a result of Itoh concerning the vanishing in
certain degrees of the local cohomology modules of the Rees algebra
of a normal ideal to prove a generalization of the
GrauertRiemenschneider Vanishing Theorem for twodimensional
CohenMacaulay varieties. Namely, we prove that if (R, m) is
a twodimensional CohenMacaulay local domain and I is an ideal
of R such that Proj R[It] is normal, then gr(I^{n},
R) is CohenMacaulay for large n. This follows from
a more general result which we will discuss concerning the depths of
gr(I^{n}, R) for large n and I a normal ideal.


94413280
Noetherian domains inside a homomorphic image of a
completion I.
By William Heinzer, Christel Rotthaus and
Sylvia M Wiegand*, swiegand@math.unl.edu.
Over the past sixty years, important examples of Noetherian
domains have been constructed from more standard Noetherian domains
using power series, homomorphic images and intersections.
In this talk, we analyse intersections of form A:=L
(R^{*} /I), where
R is a Noetherian integral domain,
L is its fraction field, R^{*}
("power series in x") is the completion of R with
respect to a nonzero
nonunit x of R, and I is an ideal of R^{*}
with the property that P R = (0)
for each P in Ass(R^{*}/I).
It is not usually true that this procedure yields a Noetherian
ring, nor is it usually easy to identify and understand the resulting
ring (even if R is the ring of polynomials in two variables over a
field). We show that A is Noetherian and computable (from R)
provided that the embedding R (R^{*}/I)_{x}
is flat.
In Christel Rotthaus' talk, "Noetherian domains inside a
homomorphic image of a completion II", she will apply
these results to construct specific examples of Noetherian local domains.


94413292
Refinements of a Conjecture of Nagata.
By Brian Harbourne*, bharbour@math.unl.edu.


94413302
Integral closure, conductors and direct
summands.
By Daniel Katz*, dlk@math.ukans.edu.
Let S be a normal Noetherian domain, w a root of a monic
irreducible polynomial over S and R the integral closure of
S[w]. Let J denote the conductor of R into S[w].
We discuss the relationship between the following conditions:
(a) J is not contained in MS[w] for all maximal
ideals M of S and
(b) S is a direct summand of R.


94413304
Depth of symmetric algebras of certain ideals.
By Mark R Johnson*, mark@math.uark.edu.
A wellknown result of Herzog, Simis and Vasconcelos guarantees the
CohenMacaulayness of the symmetric algebra for an ideal which
satisfies sliding depth and the Fitting condition F_{0}.
Without the assumption of sliding depth, we use some recent results on the
CohenMacaulayness of the blowup ring to compute in some cases
the depth of the symmetric algebra.


94413307
Divisors of a Rees algebra.
By Susan E Morey* and
Wolmer V Vasconcelos, sm26@swt.edu.
Suppose R is a Noetherian ring which has a canonical module and
I is an ideal of R. The divisors of a Rees algebra R[It]
are the rank one R[It]modules which satisfy Serre's condition
S_{2}. Two divisors of
particular importance are the canonical module of R[It] and the
fundamental divisor Ext^{n1}_{B}(IR[It], w_{B})
where B=R[T_{1}, ... , T_{n}] when I
is generated by n elements. We will discuss
properties of the divisors and how they relate to properties of R[It].
In particular we are interested in discovering when the Rees algebra is
CohenMacaulay.


94413311
Associated primes of toric initial ideals.
By Rekha R Thomas* and
Serkan Hosten, rekha@math.tamu.edu.
It is an open question to characterize those monomial
ideals that occur as initial ideals of toric ideals.
In this talk I will present some recently found special
properties that are satisfied by the associated primes of
toric initial ideals.


94413313
Fat point ideals for 8 or fewer points of
P^{2}.
By Brian Harbourne, Sandeep Holay
and Stephanie Fitchett*, sfitchet@math.duke.edu.


94413314
Strange summands of direct sums of copies of
a module.
By Roger A Wiegand*, rwiegand@math.unl.edu.
Let (R, m) be a local ring with madic
completion . For a finitely generated Rmodule M,
let S_{n} be the set of isomorphism classes of indecomposable
direct summands of the direct sum of n copies of M. Even when
M is indecomposable, the sets S_{n} can grow
large as n increases.
(However, each S_{n} is finite, and the sequence
S_{1} S_{2}
S_{3} ...
eventually stabilizes.) We will discuss the appearance of these
new indecomposable summands vis à vis splitting in the completion and
the
subtle question of which modules are extended from
Rmodules.


94413330
On the torsion freeness of symmetric powers of
ideals.
By Alexandre Tchernev*, tchernev@math.missouri.edu.


94413341
On low rank algebraic vector bundles.
By N. Mohan Kumar, Chris Peterson* and
A. Prabhakar Rao, peterson@math.wustl.edu.


94413364
Normalization of toric varieties.
By Joseph Brennan*, brennan@hazlett.math.ndsu.NoDak.edu.
The construction of the normalization of a monomial subring
of a polynomial ring will be given. Special attention will be given to
the case of subrings associated to graphs in the sense of
SimisVasconcelosVillarreal (see J. Algebra 199 (1998) 281289).


94413368
Gorenstein Modules.
By Graham J. Leuschke*, gleuschk@math.unl.edu.
A Gorenstein module for a CohenMacaulay ring R is a maximal
CohenMacaulay module G of finite injective dimension.
The concept is a generalization of the canonical module, and Gorenstein
modules enjoy several similar properties. We will discuss existence and
properties of Gorenstein modules and applications to the representation
theory of local rings.


94413378
On The GaussManin Connection.
By Herbert Kanarek*, herbert@math.unam.mx.


94413382
Some results on rational surfaces and Fano
varieties.
By Francisco J Gallego and Bangere P Purnaprajna*,
purna@math.ukans.edu.
