On the Classification of Quasihomogeneous Functions

We give a criterion for the existence of a non-degenerate quasihomogeneous polynomial in a configuration, i.e. in the space of polynomials with a fixed set of weights, and clarify the relation of this criterion to the necessary condition derived from the formula for the Poincar\'e polynomial. We further prove finiteness of the number of configurations for a given value of the singularity index. For the value 3 of this index, which is of particular interest in string theory, a constructive version of this proof implies an algorithm for the calculation of all non-degenerate configurations.Comment: 12 page

Comment on the Generation Number in Orbifold Compactifications

There has been some confusion concerning the number of $(1,1)$-forms in orbifold compactifications of the heterotic string in numerous publications. In this note we point out the relevance of the underlying torus lattice on this number. We answer the question when different lattices mimic the same physics and when this is not the case. As a byproduct we classify all symmetric $Z_N$-orbifolds with $(2,2)$ world sheet supersymmetry obtaining also some new ones.Comment: 28 pages, 9 figures not included, available in postscript at reques

Mirror Symmetry, Mirror Map and Applications to Calabi-Yau Hypersurfaces

Mirror Symmetry, Picard-Fuchs equations and instanton corrected Yukawa couplings are discussed within the framework of toric geometry. It allows to establish mirror symmetry of Calabi-Yau spaces for which the mirror manifold had been unavailable in previous constructions. Mirror maps and Yukawa couplings are explicitly given for several examples with two and three moduli.Comment: 59 pages. Some changes in the references, a few minor points have been clarifie

Track A Basic Science

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/138319/1/jia218438.pd