Smooth Compactifications of the Abel-Jacobi Section

2022/12/29 by Molcho, Sam
#14A21 #14H10 #14H40 #14T90 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2212.14375

Abstract

For θ a small generic universal stability condition of degree 0 and A a vector of integers adding up to k(2g-2), the spaces M_g,n^θ resolving the Abel-Jacobi section to the compactified Jacobian Pic^θconstructed in the work of Abreu-Pacini and Holmes-Molcho-Pandharipande-Pixton-Schmitt are observed to lie inside the space Div of Marcus and Wise, and their pullback to the rubber space of loc. cit to be smooth. This provides smooth and modular blowups \widetildeM_g,n^θ of the moduli space of stable curves on which the logarithmic double ramification cycle can be calculated by several methods, old and novel.

Related

• Fourier transforms and Abel-Jacobi theory
• On a combinatorial classification of fine compactified universal Jacobians
• Logarithmic double ramification cycles
• Compactifications of the universal Jacobian over curves with marked points
• Compactified Jacobians, Abel maps and Theta divisors