87 research outputs found
On finite generation of symbolic Rees rings of space monomial curves and existence of negative curves
In this paper, we shall study finite generation of symbolic Rees rings of the
defining ideal of the space monomial curves for pairwise
coprime integers , , such that . If such a ring
is not finitely generated over a base field, then it is a counterexample to the
Hilbert's fourteenth problem. Finite generation of such rings is deeply related
to existence of negative curves on certain normal projective surfaces. We study
a sufficient condition (Definition 3.6) for existence of a negative curve.
Using it, we prove that, in the case of , a negative curve
exists. Using a computer, we shall show that there exist examples in which this
sufficient condition is not satisfied.Comment: In the previous version, there was a serious mistake in the last
sectio
Quasi-socle ideals in a Gorenstein local ring
This paper explores the structure of quasi-socle ideals I=Q:m^2 in a
Gorenstein local ring A, where Q is a parameter ideal and m is the maximal
ideal in A. The purpose is to answer the problem of when Q is a reduction of I
and when the associated graded ring G(I) = \bigoplus_{n \geq 0}I^n/I^{n+1} is
Cohen-Macaulay. Wild examples are explored.Comment: 20 pages, minor changes, to appear in J. Pure Appl. Algebr
Almost Gorenstein rings
The notion of almost Gorenstein ring given by Barucci and Fr{\"o}berg
\cite{BF} in the case where the local rings are analytically unramified is
generalized, so that it works well also in the case where the rings are
analytically ramified. As a sequel, the problem of when the endomorphism
algebra \m : \m of \m is a Gorenstein ring is solved in full generality,
where \m denotes the maximal ideal in a given Cohen-Macaulay local ring of
dimension one. Characterizations of almost Gorenstein rings are given in
connection with the principle of idealization. Examples are explored
The Aligned Model
In Calabi-Yau string compactification, it is pointed out that there exists a
new type of model (the aligned
model) in which the differs from the standard and also from the
flipped . With the aid of the discrete symmetry suggested from Gepner
model, we construct a simple and phenomenologically interesting
three-generation model with the aligned gauge symmetry.
The triplet-doublet splitting problem can be solved. It is also found that
there is a realistic solution for solar neutrino problem and for the -problem. At low energies this model is in accord with the minimal
supersymmetric standard model except for the existence of singlet fields with
masses of TeV.Comment: LaTeX 24 page
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