Multiple covers and the integrality conjecture for rational curves in Calabi-Yau threefolds
| dc.creator | Bryan, Jim | |
| dc.creator | Katz, Sheldon | |
| dc.creator | Leung, Naichung Conan | |
| dc.date | 1999-11-09 | |
| dc.date.accessioned | 2026-07-07T05:31:31Z | |
| dc.date.available | 2026-07-07T05:31:31Z | |
| dc.description | We study the contribution of multiple covers of an irreducible rational curve C in a Calabi-Yau threefold Y to the genus 0 Gromov-Witten invariants in the following cases. (1) If the curve C has one node and satisfies a certain genericity condition, we prove that the contribution of multiple covers of degree d is given by the sum of all 1/n^3 where n divides d. (2) For a smoothly embedded contractable curve C in Y we define schemes C_i for i=1,...,l where C_i is supported on C and has multiplicity i, and the integer l (0<l<7) is Kollar's invariant ``length''. We prove that the contribution of multiple covers of C of degree d is given by the sum of k_{d/n}/n^3 where n divides d and where k_i is the multiplicity of C_i in its Hilbert scheme (and k_i=0 if i>l). In the latter case we also get a formula for arbitrary genus. These results show that the curve C contributes an integer amount to the so-called instanton numbers that are defined recursively in terms of the Gromov-Witten invariants and are conjectured to be integers. | |
| dc.description | uses diagrams.sty | |
| dc.identifier | https://arxiv.org/abs/math/9911056 | |
| dc.identifier | http://arxiv.org/abs/math/9911056 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/79370 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Differential Geometry | |
| dc.subject | Symplectic Geometry | |
| dc.subject | 14N35;53D45 | |
| dc.title | Multiple covers and the integrality conjecture for rational curves in Calabi-Yau threefolds | |
| dc.type | text |