Degree zero Gromov--Witten invariants for smooth curves

Di Yang

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arXiv · 2208.02095

Degree zero Gromov--Witten invariants for smooth curves

Di Yang

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Abstract

For a smooth projective curve, we derive a closed formula for the generating series of its Gromov--Witten invariants in genus $g$ and degree zero. It is known that the calculation of these invariants can be reduced to that of the $\lambda_g$ and $\lambda_{g-1}$ integrals on the moduli space of stable algebraic curves. The closed formula for the $\lambda_g$ integrals is given by the $\lambda_g$ conjecture, proved by Faber and Pandharipande. We compute in this paper the $\lambda_{g-1}$ integrals via solving the degree zero limit of the loop equation associated to the complex projective line.

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BibTeX RIS

Di Yang. 2022-08-03. Degree zero Gromov--Witten invariants for smooth curves. https://arxiv.org/abs/2208.02095

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