Mathematical Research Letters

Volume 26 (2019)

Number 5

Counting conics on sextic $4$-folds

Pages: 1343 – 1357



Yalong Cao (Kavli Institute for the Physics and Mathematics of the Universe, University of Tokyo, Kashiwa-shi, Chiba, Japan)


We study rational curves of degree two on a smooth sextic $4$-fold and their counting invariant defined using Donaldson–Thomas theory of Calabi–Yau $4$-folds. By comparing it with the corresponding Gromov–Witten invariant, we verify a conjectural relation between them proposed by the author, Maulik and Toda.

Received 18 November 2018

Accepted 25 December 2018

Published 27 November 2019