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 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Hyperelliptic limits of hypersurfaces through canonical curves and ribbons
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by Alexander Polishchuk and Eric Rains;
Trans. Amer. Math. Soc. 378 (2025), 5087-5123
DOI: https://doi.org/10.1090/tran/9417
Published electronically: March 19, 2025

Abstract:

We describe explicitly all hyperelliptic limits of hypersurfaces through smooth canonical curves of genus $g$ in $\mathbb {P}^{g-1}$. Also, we construct an open embedding of the blow-up of a $PGL_g$-bundle over the moduli space of curves of genus $g$ along the hyperelliptic locus into the blow-up of the canonical Hilbert scheme of $\mathbb {P}^{g-1}$ along the closure of the locus of canonical ribbons, which are certain double thickenings of rational normal curves introduced and studied by Bayer and Eisenbud [Trans. Amer. Math. Soc. 347 (1995), pp. 719–756].
References
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Bibliographic Information
  • Alexander Polishchuk
  • Affiliation: University of Oregon, Eugene, Oregon; National Research University Higher School of Economics, Moscow, Russia
  • MR Author ID: 339630
  • Email: apolish@uoregon.edu
  • Eric Rains
  • Affiliation: California Institute of Technology, Pasadena, California
  • MR Author ID: 311477
  • ORCID: 0000-0002-9915-0919
  • Email: rains@caltech.edu
  • Received by editor(s): January 1, 2024
  • Received by editor(s) in revised form: July 29, 2024, and January 17, 2025
  • Published electronically: March 19, 2025
  • Additional Notes: The research of the first author was partially supported by the NSF grants DMS-2001224, NSF grant DMS-2349388, by the Simons Travel grant MPS-TSM-00002745, and within the framework of the HSE University Basic Research Program.
  • Dedicated: To David Eisenbud, an offering in ribbons
  • © Copyright 2025 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 378 (2025), 5087-5123
  • MSC (2020): Primary 14H10; Secondary 14C05
  • DOI: https://doi.org/10.1090/tran/9417