Remarks on the Griffiths infinitesimal invariant of algebraic curves

TL;DR

This paper investigates the Griffiths infinitesimal invariant of algebraic curves, focusing on two canonical normal functions on the moduli space of genus 4 curves, and explores their vanishing criteria.

Contribution

It provides new insights into the vanishing conditions of Griffiths infinitesimal invariants for specific normal functions on genus 4 curves.

Findings

Identifies vanishing criteria for Griffiths invariants

Analyzes two canonical normal functions on moduli space

Focuses on genus 4 algebraic curves

Abstract

We study two canonically defined admissible normal functions on the moduli space of smooth genus 4 algebraic curves including the Ceresa normal function. In particular, we study the vanishing criteria for the Griffiths infinitesimal invariants of both normal functions over a specific family of curves.