MSP theory for smooth Calabi-Yau threefolds in weighted $\mathbb{P}^4$

TL;DR

This paper extends the MSP theory to smooth Calabi-Yau threefolds in weighted projective spaces, providing a new framework for understanding their geometric and enumerative properties.

Contribution

It develops the theory of N-mixed-spin-P fields specifically for Fermat-type hypersurfaces in weighted projective spaces, expanding the applicability of MSP theory beyond the quintic threefold.

Findings

Established MSP theory for specific weighted projective hypersurfaces

Generalized previous MSP frameworks to new Calabi-Yau threefolds

Provides tools for future enumerative geometry studies

Abstract

We develop the theory of $N$-mixed-spin-$P$ fields for Fermat-type hypersurfaces in $\mathbb{P}(1,1,1,1,2)$, $\mathbb{P}(1,1,1,1,4)$, and $\mathbb{P}(1,1,1,1,4)$, following the theory developed in arXiv:1809.08806 for the quintic threefold.