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Transactions of the American Mathematical Society

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Invariants of stable quasimaps with fields


Authors: Huai-Liang Chang and Mu-lin Li
Journal: Trans. Amer. Math. Soc. 373 (2020), 3669-3691
MSC (2010): Primary 14P20, 14N35
DOI: https://doi.org/10.1090/tran/8011
Published electronically: February 11, 2020
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Abstract: The moduli of quasimaps to $ \mathbb{P}^n$ with P fields are constructed for the case of an arbitrary smooth hypersurface $ X\subset \mathbb{P}^n$, along with the virtual fundamental class via Kiem and Li's cosection localization. The class is shown to coincide with the virtual class of the moduli of quasimaps to $ X$. This generalizes Chang and Li's numerical identity to the cycle level and from Gromov-Witten invariants to quasimap invariants.


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Additional Information

Huai-Liang Chang
Affiliation: Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
Email: mahlchang@ust.hk

Mu-lin Li
Affiliation: College of Mathematics and Econometrics, Hunan University, Hunan, 410006 People’s Republic of China
Email: mulin@hnu.edu.cn

DOI: https://doi.org/10.1090/tran/8011
Received by editor(s): June 17, 2018
Received by editor(s) in revised form: February 8, 2019, and September 23, 2019
Published electronically: February 11, 2020
Additional Notes: The first author was partially supported by grants 16301515 and 16301717 from the general research fund of Hong Kong’s Research Grants Committee.
The second author was partially supported by the Start-up Fund of Hunan University.
Mu-Lin Li is the corresponding author
Article copyright: © Copyright 2020 American Mathematical Society