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On the Geometry and Homology of Certain Simple Stratified Varieties

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arxiv math/0210394 v1 pith:MDYTCZOM submitted 2002-10-24 math.AG hep-thmath-phmath.MP

Tristan Hubsch , Abdul Rahman This is my paper · ORCID
classification math.AGhep-thmath-phmath.MP
keywords varietycertainfloppedgroundhomologystatestratifiedtheory
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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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Cited by 2 Pith papers

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  1. Beyond Algebraic Superstring Compactification

    hep-th 2025-02 conditional novelty 5.0 of 10

    Calabi-Yau compactifications and mirror symmetry are conjecturally extended to non-algebraic toric spaces using Laurent deformations and the 'intrinsic limit' completion.

  2. Chern Characteristics and Todd-Hirzebruch Identities for Transpolar Pairs of Toric Spaces

    hep-th 2024-03 unverdicted novelty 5.0 of 10

    Transpolar pairs involving VEX multitopes yield smooth toric spaces whose Chern classes satisfy Todd-Hirzebruch identities and belong to deformation families of generalized complete intersections.

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