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
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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