4 papers · 1 filter
Logarithmic intersections of double ramification cycles
David Holmes, Rosa Schwarz
We describe a theory of logarithmic Chow rings and tautological subrings for logarithmically smooth algebraic stacks, via a generalisation of the notion of piecewise-polynomial fun…
Fields of definition of curves of a given degree
David Holmes, Nick Rome
Kontsevich and Manin gave a formula for the number of rational plane curves of degree through points in general position in the plane. When these points hav…
Multiplicativity of the double ramification cycle
David Holmes, Aaron Pixton, Johannes Schmitt
The double ramification cycle satisfies a basic multiplicative relation DRC(a).DRC(b) = DRC(a).DRC(a + b) over the locus of compact-type curves, but this relation fails in the Chow…
Quasi-compactness of Néron models, and an application to torsion points
David Holmes
We prove that Néron models of jacobians of generically-smooth nodal curves over bases of arbitrary dimension are quasi-compact (hence of finite type) whenever they exist. We give a…