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Genus three Ceresa cycles and limit of archimedean heights

Souvik Goswami, Irene Spelta

Abstract

For a family of smooth, projective curves of genus three, we interpret the limit of archimedean height pairings of Ceresa cycles associated with the family in terms of the archimedean pairing of algebraic cycles naturally associated with the central fiber of the family.

Genus three Ceresa cycles and limit of archimedean heights

Abstract

For a family of smooth, projective curves of genus three, we interpret the limit of archimedean height pairings of Ceresa cycles associated with the family in terms of the archimedean pairing of algebraic cycles naturally associated with the central fiber of the family.

Paper Structure

This paper contains 18 sections, 12 theorems, 100 equations, 1 figure.

Table of Contents

  1. Preliminaries
  2. Mixed Hodge structures
  3. Deligne splitting
  4. Nodal curves and Jacobians
  5. Jacobian of a nodal curve
  6. Abel Jacobi map on stable curves
  7. Degenerations
  8. Degeneration of curves and their Jacobians
  9. Survey of general degenerations of geometric origin
  10. Degeneration of smooth projective curves and MHS
  11. The case of central irreducible nodal curve
  12. The case of central reducible curve
  13. Biextension mixed Hodge structure and its variation
  14. Geometric biextension
  15. Abstract degeneration of biextension variations
  16. ...and 3 more sections

Key Result

Corollary 1.5

A short exact sequence induces a short exact sequence on graded pieces $\blacktriangleleft$$\blacktriangleleft$

Figures (1)

  • Figure 1: Biextension diagram

Theorems & Definitions (34)

  • Definition 1.1
  • Example 1.2
  • Definition 1.3
  • Definition 1.4
  • Corollary 1.5
  • Remark 1.6
  • Lemma 1.7
  • proof
  • Theorem 2.1
  • Definition 3.1
  • ...and 24 more