#### Volume 18, issue 2 (2014)

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The genus $0$ Gromov–Witten invariants of projective complete intersections

### Aleksey Zinger

Geometry & Topology 18 (2014) 1035–1114
##### Abstract

We describe the structure of mirror formulas for genus $0$ Gromov–Witten invariants of projective complete intersections with any number of marked points and provide an explicit algorithm for obtaining the relevant structure coefficients. As an application, we give explicit closed formulas for the genus $0$ Gromov–Witten invariants of Calabi–Yau complete intersections with $3$ and $4$ constraints. The structural description alone suffices for some qualitative applications, such as vanishing results and the bounds on the growth of these invariants predicted by R Pandharipande. The resulting theorems suggest intriguing conjectures relating GW–invariants to the energy of pseudoholomorphic maps and the expected dimensions of their moduli spaces.

##### Keywords
Gromov–Witten invariants, complete intersections
Primary: 14N35
Secondary: 53D45
##### Publication
Received: 25 January 2013
Revised: 1 October 2013
Accepted: 24 November 2013
Published: 7 April 2014
Proposed: Jim Bryan
Seconded: Richard Thomas, Lothar Goettsche
##### Authors
 Aleksey Zinger Department of Mathematics SUNY Stony Brook Stony Brook, NY 11794-3651 USA http://www.math.sunysb.edu/~azinger