P. Spelier

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math.AG2026

Splitting and loop theorems in logarithmic Gromov--Witten theory

Leo Herr, David Holmes, Pim Spelier

We define a new theory of logarithmic Gromov--Witten invariants allowing negative contact orders using pierced logarithmic curves. We prove that these classes satisfy logarithmic b…

math.AG2025

Splitting formulas for the logarithmic double ramification cycle

Pim Spelier

The logarithmic double ramification cycle is roughly a logarithmic Gromov--Witten invariant of $P^{1}$ . For classical Gromov--Witten invariants, formulas for the pullback al…

math.AG2024

The log Grothendieck ring of varieties

Andreas Gross, Leo Herr, David Holmes +2

We define a Grothendieck ring of varieties for log schemes. It is generated by one additional class `` $P$ '' over the usual Grothendieck ring. We show the naïve definition of log Ho…

math.AG2024

Logarithmic tautological rings of the moduli spaces of curves

Rahul Pandharipande, Dhruv Ranganathan, Johannes Schmitt +1

We define the logarithmic tautological rings of the moduli spaces of Deligne-Mumford stable curves (together with a set of additive generators lifting the decorated strata classes…

math.AG2024

Polynomiality of the double ramification cycle

Pim Spelier

Let $A = (a_{1}, \dots, a_{n}) \in Z^{n}$ be a sequence with sum $k (2 g - 2 + n)$ . The double ramification cycle $DR_{g} (A) \in CH^{g} (M ˉ_{g, n})$ is the vir…

math.AG2023

Logarithmic cohomological field theories

David Holmes, Pim Spelier

We introduce a new logarithmic structure on the moduli stack of stable curves, admitting logarithmic gluing maps. Using this we define cohomological field theories taking values in…