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- Daniel B. Grünberg, Pieter Moree, Don Zagier
- Experimental Mathematics
- 2008

We study the integer sequence v n of numbers of lines in hypersurfaces of degree 2n − 3 of P n , n > 1. We prove a number of congruence properties of these numbers of several different types. Furthermore, the asymptotics of the v n are described (in an appendix by Don Zagier). An attempt is made at a similar analysis of two other enumerative sequences: the… (More)

We prove the integrality of the open instanton numbers in two examples of counting holomorphic disks on local Calabi-Yau threefolds: the resolved conifold and the degenerate P 1 × P 1. Given the B-model superpotential, we extract by hand all Gromow-Witten invariants in the expansion of the A-model superpo-tential. The proof of their integrality relies on… (More)

We review the properties of characters of the N=4 SCA in the context of a non-linear sigma model on K3, how they are used to span the orbits, and how the orbits produce topological invariants like the elliptic genus. We derive the same expression for the K3 elliptic genus using three different Gepner models (1 6 , 2 4 and 4 3 theories), detailing the orbits… (More)

We present an overview of Gromov-Witten theory and its links with string theory compactifications, focussing on the GW potential as the generating function for topological string amplitudes at genus g. Restricting to Calabi-Yau target spaces, we give a complete derivation of the GW potential, discuss problems of multicovers and the infinite product… (More)

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