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General GLSM Invariants and Their Cohomological Field Theories

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arxiv 2006.12182 v2 pith:VJNMI4I6 submitted 2020-06-22 math.AG hep-th

David Favero , Bumsig Kim This is my paper · ORCID
classification math.AGhep-th
keywords generalclasscohomologicalfieldglsminvariantsmatrixanalogue
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We construct GLSM invariants for a general choice of stability in both the narrow and broad sector cases and prove they form a Cohomological Field Theory. This is obtained by forming the analogue of a virtual fundamental class which lives in the local cohomology of the twisted Hodge complex. This general construction comes from the use of two new ingredients. First, the use of the Thom-Sullivan and Godement resolutions applied to matrix factorizations are introduced to handle poorly behaved (non-separated) moduli spaces. Second, a localized Chern character map built from the Atiyah class of a matrix factorization is utilized to forgo the use of Hochschild homology.

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  1. A topological Chern character for matrix factorizations

    math.AG 2026-07 conditional novelty 6.0 of 10

    A topological Chern character from matrix-factorization K-theory to critical cohomology is constructed for global Landau-Ginzburg models, along with a Grothendieck-Riemann-Roch theorem.

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