A New Method for Finding Vacua in String Phenomenology

One of the central problems of string-phenomenology is to find stable vacua in the four dimensional effective theories which result from compactification. We present an algorithmic method to find all of the vacua of any given string-phenomenological system in a huge class. In particular, this paper reviews and then extends hep-th/0606122 to include various non-perturbative effects. These include gaugino condensation and instantonic contributions to the superpotential.Comment: 27 pages, 5 .eps figures. V2: Minor corrections, reference adde

Deterministically Computing Reduction Numbers of Polynomial Ideals

We discuss the problem of determining reduction number of a polynomial ideal I in n variables. We present two algorithms based on parametric computations. The first one determines the absolute reduction number of I and requires computation in a polynomial ring with (n-dim(I))dim(I) parameters and n-dim(I) variables. The second one computes via a Grobner system the set of all reduction numbers of the ideal I and thus in particular also its big reduction number. However,it requires computations in a ring with n.dim(I) parameters and n variables.Comment: This new version replaces the earlier version arXiv:1404.1721 and it has been accepted for publication in the proceedings of CASC 2014, Warsaw, Polna

Generating Non-Linear Interpolants by Semidefinite Programming

Interpolation-based techniques have been widely and successfully applied in the verification of hardware and software, e.g., in bounded-model check- ing, CEGAR, SMT, etc., whose hardest part is how to synthesize interpolants. Various work for discovering interpolants for propositional logic, quantifier-free fragments of first-order theories and their combinations have been proposed. However, little work focuses on discovering polynomial interpolants in the literature. In this paper, we provide an approach for constructing non-linear interpolants based on semidefinite programming, and show how to apply such results to the verification of programs by examples.Comment: 22 pages, 4 figure

Torsion free modules and simple curve singularities

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Constant Milnor number implies constant multiplicity for quasihomogeneous singularities

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A remark on the paper of A. Tannenbaum

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The dimension of smoothing components

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Families of varieties with prescribed singularities

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Cohen-Macaulay modules on hypersurface singularities. 2 Dedicated to Egbert Brieskorn

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