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We study the weighted spectrum and vanishing cohomology for several classes of isolated hypersurface singularities, and how they contribute to the limiting mixed Hodge structure of a smoothing. Applications are given to several types of singularities arising in KSBA and GIT compactifications and mirror symmetry, including nodes on odd-dimensional hypersurfaces, k-log-canonical and k-rational singularities, and singularities with Calabi-Yau tail.

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Hodge Theory of Degenerations, (II): Vanishing Cohomology and Geometric Applications

  • 会议论文

  • 发表日期：

    2025年

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  • Matt Kerr,
  • Radu Laza

摘要

We study the weighted spectrum and vanishing cohomology for several classes of isolated hypersurface singularities, and how they contribute to the limiting mixed Hodge structure of a smoothing. Applications are given to several types of singularities arising in KSBA and GIT compactifications and mirror symmetry, including nodes on odd-dimensional hypersurfaces, k-log-canonical and k-rational singularities, and singularities with Calabi-Yau tail.