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GEOMETRIC CONSTRUCTION OF QUOTIENTS G/H IN SUPERSYMMETRY

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It was proved by the first-named author and Zubkov [13] that given an affine algebraic supergroup \( \mathbbm{G} \) and a closed sub-supergroup ℍ over an arbitrary field of characteristic ≠ 2, the faisceau \( \mathbbm{G}\tilde{/}\mathrm{\mathbb{H}} \) (in the fppf topology) is a superscheme, and is, therefore, the quotient superscheme \( \mathbbm{G}/\mathrm{\mathbb{H}} \), which has some desirable properties, in fact. We reprove this, by constructing directly the latter superscheme \( \mathbbm{G}/\mathrm{\mathbb{H}} \). Our proof describes explicitly the structure sheaf of \( \mathbbm{G}/\mathrm{\mathbb{H}} \), and reveals some new geometric features of the quotient, that include one which was desired by Brundan [2], and is shown in general, here for the first time.

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Authors and Affiliations

  1. Institute of Mathematics, University of Tsukuba, Ibaraki, 305-8571, Japan

    AKIRA MASUOKA

  2. Graduate School of Pure and Applied Sciences, University of Tsukuba, Ibaraki, 305-8571, Japan

    YUTA TAKAHASHI

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  1. AKIRA MASUOKA
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  2. YUTA TAKAHASHI
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Correspondence to AKIRA MASUOKA.

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Akira Masuoka is supported by JSPS Grant-in-Aid for Scientific Research (C) 17K05189.

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MASUOKA, A., TAKAHASHI, Y. GEOMETRIC CONSTRUCTION OF QUOTIENTS G/H IN SUPERSYMMETRY. Transformation Groups 26, 347–375 (2021). https://doi.org/10.1007/s00031-020-09583-3

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