arXiv subjects

Shuai Guo

Publications and source records attributed to Shuai Guo.

58 records · Page 4Linked to original sources

arXiv2017

The Genus-One Global Mirror Theorem for the Quintic Threefold

We prove the genus-one restriction of the all-genus Landau-Ginzburg/Calabi-Yau conjecture of Chiodo and Ruan, stated in terms of the geometric quantization of an explicit symplectomorphism determined by genus-zero invariants. This provides the first evidence supporting the higher-genus Landau-Ginzburg/Calabi-Yau correspondence for the quintic threefold, and exhibits the first instance of the "genus zero controls higher genus" principle, in the sense of Givental's quantization formalism, for non-semisimple cohomological field theories.

math.AG↗

arXiv2017

Genus-One Mirror Symmetry in the Landau-Ginzburg Model

We prove an explicit formula for the genus-one Fan-Jarvis-Ruan-Witten invariants associated to the quintic threefold, verifying the genus-one mirror conjecture of Huang, Klemm, and Quackenbush. The proof involves two steps. The first step uses localization on auxiliary moduli spaces to compare the usual Fan-Jarvis-Ruan-Witten invariants with a semisimple theory of twisted invariants. The second step uses the genus-one formula for semisimple cohomological field theories to compute the twisted invariants explicitly.

math.AG↗

arXiv2016

Virasoro constraints and polynomial recursion for the linear Hodge integrals

The Hodge tau-function is a generating function for the linear Hodge integrals. It is also a tau-function of the KP hierarchy. In this paper, we first present the Virasoro constraints for the Hodge tau-function in the explicit form of the Virasoro equations. The expression of our Virasoro constraints is simply a linear combination of the Virasoro operators, where the coefficients are restored from a power series for the Lambert W function. Then, using this result, we deduce a simple version of the Virasoro constraints for the linear Hodge partition function, where the coefficients are restored from the Gamma function. Finally, we establish the equivalence relation between the Virasoro constraints and polynomial recursion formula for the linear Hodge integrals.

math-ph↗

arXiv2012

Gopakumar-Vafa BPS invariants, Hilbert schemes and quasimodular forms. I

We prove a closed formula for leading Gopakumar- Vafa BPS invariants of local Calabi-Yau geometries given by the canonical line bundles of toric Fano surfaces. It shares some similar features with Goettsche-Yau-Zaslow formula: Connection with Hilbert schemes, connection with quasimodular forms, and quadratic property after suitable transformation. In Part I of this paper we will present the case of projective plane, more general cases will be presented in Part II.

math.AG↗