On the Geometry and Homology of Certain Simple Stratified Varieties

Details On the Geometry and Homology of Certain Simple Stratified Varieties On the Geometry and Homology of Certain Simple Stratified Varieties

2002-10-24

arxiv.org/abs/math/0210394v1

J.Geom.Phys. 53 (2005) 31-48

Mathematics

Algebraic Geometry

LaTeX 2e, 18 pages, 4 figures

Scientific paper

We study certain mild degenerations of algebraic varieties which appear in the analysis of a large class of supersymmetric theories, including superstring theory. We analyze Witten's sigma-model and find that the non-transversality of the superpotential induces a singularization and stratification of the ground state variety. This stratified variety (the union of the singular ground state variety and its exo-curve strata) admit homology groups which, excepting the middle dimension, satisfy the "Kahler package" of requirements, extend the "flopped" pair of small resolutions to an "(exo)flopped" triple, and is compatible with mirror symmetry and string theory. Finally, we revisit the conifold transition as it applies to our formalism.

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