Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Remarks on eigenspectra of isolated singularities

Ben Castor, Haohua Deng, Matt Kerr, Gregory Pearlstein

Abstract

We introduce a simple calculus, extending a variant of the Steenbrink spectrum, for describing Hodge-theoretic invariants of (smoothings of) isolated singularities with (relative) automorphisms. After computing these "eigenspectra" in the quasi-homogeneous case, we give three applications to singularity bounding and monodromy of VHS.

Remarks on eigenspectra of isolated singularities

Abstract

We introduce a simple calculus, extending a variant of the Steenbrink spectrum, for describing Hodge-theoretic invariants of (smoothings of) isolated singularities with (relative) automorphisms. After computing these "eigenspectra" in the quasi-homogeneous case, we give three applications to singularity bounding and monodromy of VHS.
Paper Structure (5 sections, 11 theorems, 41 equations)

This paper contains 5 sections, 11 theorems, 41 equations.

Table of Contents

  1. $G$-spectra and eigenspectra
  2. Quasihomogeneous singularities with automorphism
  3. Bounding nodes on Calabi-Yau hypersurfaces
  4. Cyclic covers of $\mathbb{P}^1$
  5. Hyperplane configurations and Dolgachev's conjecture

Key Result

Proposition A.3

We have the commutative diagram\xymatrix@C=13pt{\to \mathbb{H}^k(X_0,\imath^*\mathcal{K}^{\bullet}) \ar [r]^{\mathrm{sp}} \ar [d]^{\rho} & \mathbb{H}^k(X_0,\psi_f\mathcal{K}^{\bullet}) \ar [r]^{\mathrm{can}} \ar [d]^{\rho} & \mathbb{H}^k(X_0,\phi_f\mathcal{K}^{\bullet}) \ar [r]^{\delta\mspace{25mu}}

Theorems & Definitions (35)

  • Proposition A.3
  • Remark A.4
  • Definition A.8
  • Corollary A.9
  • Definition A.11
  • Definition A.12
  • Remark A.13
  • Proposition B.3
  • proof : Sketch
  • Corollary B.7
  • ...and 25 more