Curve counting in genus one: Elliptic singularities and relative geometry

Autor:	Navid Nabijou, Luca Battistella, Dhruv Ranganathan
Rok vydání:	2021
Předmět:	Mathematics - Algebraic Geometry Mathematics::Algebraic Geometry Algebra and Number Theory Genus (mathematics) Geometry Gravitational singularity Geometry and Topology 14N35 14H10 Mathematics::Symplectic Geometry Mathematics
Zdroj:	Algebraic Geometry. :637-679
ISSN:	2214-2584
Popis:	We construct and study the reduced, relative, genus one Gromov--Witten theory of very ample pairs. These invariants form the principal component contribution to relative Gromov--Witten theory in genus one and are relative versions of Zinger's reduced Gromov--Witten invariants. We relate the relative and absolute theories by degeneration of the tangency conditions, and the resulting formulas generalise a well-known recursive calculation scheme put forward by Gathmann in genus zero. The geometric input is a desingularisation of the principal component of the moduli space of genus one logarithmic stable maps to a very ample pair, using the geometry of elliptic singularities. Our study passes through general techniques for calculating integrals on logarithmic blowups of moduli spaces of stable maps, which may be of independent interest. Comment: 38 pages, 11 figures, comments welcome! v2: exposition improved thanks to the referee's comments. Final version to appear in Algebraic Geometry
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b4b8fc4c70027d2ef21bfb275b76e526 https://doi.org/10.14231/ag-2021-020 Zobrazit plný text záznamu