Gromov-Witten Theory of Complete Intersections via Nodal Invariants

We provide an inductive algorithm computing Gromov-Witten invariants in all genera with arbitrary insertions of all smooth complete intersections in projective space. We also prove that all Gromov-Witten classes of all smooth complete intersections in projective space belong to the tautological ring...

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Bibliographic Details
Published inarXiv.org
Main Authors Argüz, Hülya, Bousseau, Pierrick, Pandharipande, Rahul, Zvonkine, Dimitri
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 11.01.2023
Subjects
Algorithms
Degeneration
Homology
Intersections
Invariants
Mathematics - Algebraic Geometry
Mathematics - Symplectic Geometry
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Summary:We provide an inductive algorithm computing Gromov-Witten invariants in all genera with arbitrary insertions of all smooth complete intersections in projective space. We also prove that all Gromov-Witten classes of all smooth complete intersections in projective space belong to the tautological ring of the moduli space of stable curves. The main idea is to show that invariants with insertions of primitive cohomology classes are controlled by their monodromy and by invariants defined without primitive insertions but with imposed nodes in the domain curve. To compute these nodal Gromov-Witten invariants, we introduce the new notion of nodal relative Gromov-Witten invariants. We then prove a nodal degeneration formula and a relative splitting formula. These results for nodal relative Gromov-Witten theory are stated in complete generality and are of independent interest.
ISSN:2331-8422
DOI:10.48550/arxiv.2109.13323