Communications in Analysis and Geometry

Volume 31 (2023)

Number 6

On a conjecture of Huang–Lian–Yau–Yu

Pages: 1341 – 1352

DOI: https://dx.doi.org/10.4310/CAG.2023.v31.n6.a1

Authors

Tsung-Ju Lee (Department of Mathematics, National Cheng Kung University, Tainan, Taiwan)

Bong H. Lian (Department of Mathematics, Brandeis University, Waltham, Massachusetts, U.S.A.)

Dingxin Zhang (Yau Mathematical Sciences Center, Tsinghua University, Beijing, China)

Abstract

We verify a formula on the solution rank of the tautological system arising from ample complete intersections in a projective homogeneous space of a semisimple group conjectured by Huang–Lian–Yau–Yu $\href{https://doi.org/10.48550/arXiv.1801.01194}{[1]}$. As an application, we prove the existence of the rank one point for such a system, where mirror symmetry is expected.

Received 3 March 2020

Accepted 28 April 2021

Published 9 August 2024