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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Invariants of stable quasimaps with fields
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by Huai-Liang Chang and Mu-lin Li PDF
Trans. Amer. Math. Soc. 373 (2020), 3669-3691 Request permission

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
  • MR Author ID: 912404
  • Email: mahlchang@ust.hk
  • Mu-lin Li
  • Affiliation: College of Mathematics and Econometrics, Hunan University, Hunan, 410006 People’s Republic of China
  • MR Author ID: 1303502
  • Email: mulin@hnu.edu.cn
  • 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
  • © Copyright 2020 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 373 (2020), 3669-3691
  • MSC (2010): Primary 14P20, 14N35
  • DOI: https://doi.org/10.1090/tran/8011
  • MathSciNet review: 4082252