Normal Functions and the Geometry of Moduli Spaces of Curves

Abstract

In this paper normal functions (in the sense of Griffiths) are used to solve and refine geometric questions about moduli spaces of curves. The first application is to a problem posed by Eliashberg: compute the class in the cohomology of M_{g,n}^c of the pullback of the zero section of the universal jacobian along the section that takes [C;x_1,...,x_n] to Sum d_j x_j in Jac (C), where d_1 + ... + d_n = 0. The second application is to slope inequalities of the type discovered by Moriwaki. There is also a discussion of height jumping and its relevance to slope inequalilties.

Updated to published version. Also added publication information

References in corpus (2)

• Chow rings and decomposition theorems for families of K3 surfaces and Calabi-Yau hypersurfaces
• An Exponential History of Functions with Logarithmic Growth

Cited by in corpus (28)

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• Pixton's double ramification cycle relations
• Stable maps to rational curves and the relative Jacobian
• Extending the Double Ramification Cycle using Jacobians
• Faltings delta-invariant and semistable degeneration
• The zero section of the universal semiabelian variety, and the double ramification cycle
• Infinitesimal structure of the pluricanonical double ramification locus
• Quadratic double ramification integrals and the noncommutative KdV hierarchy
• Integrability, Quantization and Moduli Spaces of Curves
• The double ramification cycle and the theta divisor
• Pixton's formula and Abel-Jacobi theory on the Picard stack
• Extensions of the universal theta divisor
• Positivity of the height jump divisor
• Compactified universal jacobian and the double ramification cycle
• The pullback of a theta divisor to M_{g,n}
• Extended $r$-spin theory in all genera and the discrete KdV hierarchy
• Polynomial families of tautological classes on ${\mathcal{M}}_{g,n}^{rt}$
• Jumps in the Archimedean Height
• A conjectural formula for $D{R}_g(a,-a){\lambda }_g$
• Normal functions and the height of Gross-Schoen cycles
• Jumps in the height of the Ceresa cycle
• Loci of curves with subcanonical points in low genus
• Tautological classes with twisted coefficients
• On the height of Gross-Schoen cycles in genus three
• Frobenius' theta function and Arakelov invariants in genus three
• Tropical Normal Functions -- Higher Abel-Jacobi Invariants of Tropical cycles
• Chern-Weil theory for line bundles with the family Arakelov metric