A Gromov-Witten approach to $G$-equivariant birational invariants
Abstract
In arXiv:2404.19088, we initiated a program linking birational invariants with smooth ones and offering new interpretations of classical invariants, such as the Kervaire-Milnor invariants. Here, we rely on the profound geometric reasoning provided by Lupercio and Uribe in the early 00s to establish a connection between Chen-Ruan cohomology and several -birational invariants introduced in the pioneering works Kontsevich, Kresch, Pestun, Tschinkel, along with presenting applications. Combined with the theory of atoms by Katzarkov, Kontsevich, Pantev, and Yu, the proposal in this paper program will lead to a theory of equivariant atoms.
Cite
@article{arxiv.2405.07322,
title = {A Gromov-Witten approach to $G$-equivariant birational invariants},
author = {Leonardo F. Cavenaghi and Lino Grama and Ludmil Katzarkov},
journal= {arXiv preprint arXiv:2405.07322},
year = {2025}
}
Comments
This paper contained many ideas to be developed. Part of the results and conjectures proposed in this work were developed in arXiv:2509.15831 by other authors. To avoid overlap, the remaining shall appear elsewhere in a series of papers with several authors