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Gorenstein curve singularities of genus three

Luca Battistella

Abstract

We classify the analytic germs of isolated Gorenstein curve singularities of genus three, and relate them to the connected components of strata of abelian differentials.

Gorenstein curve singularities of genus three

Abstract

We classify the analytic germs of isolated Gorenstein curve singularities of genus three, and relate them to the connected components of strata of abelian differentials.
Paper Structure (15 sections, 1 theorem, 31 equations)

This paper contains 15 sections, 1 theorem, 31 equations.

Table of Contents

  1. Geometric context
  2. The canonical linear series on smooth curves
  3. Theta characteristics and singular curves
  4. Bitangents
  5. Projective duality
  6. Harris
  7. Isolated Gorenstein curve singularities
  8. Rosenlicht
  9. Serre
  10. Stevens
  11. Smyth
  12. Semistable tails and differentials
  13. (Compact) strata of holomorphic differentials
  14. Crimping spaces and moduli of singular curves
  15. Algebraic classification

Key Result

Theorem 1

There are seven families of isolated Gorenstein singularities of genus three, each corresponding to a connected component of a stratum of abelian differentials of genus three.

Theorems & Definitions (6)

  • Theorem
  • Remark 1.1
  • Conjecture 1.2: differential descent
  • Remark 2.1
  • Remark 2.2
  • Remark 2.3