Limit linear series and ranks of multiplication maps
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- by Fu Liu, Brian Osserman, Montserrat Teixidor i Bigas and Naizhen Zhang PDF
- Trans. Amer. Math. Soc. 374 (2021), 367-405 Request permission
Abstract:
We develop a new technique to study ranks of multiplication maps for linear series via limit linear series and degenerations to chains of elliptic curves. We prove an elementary criterion and apply it to proving cases of the Maximal Rank Conjecture. We give a new proof of the case of quadrics, and also treat several families in the case of cubics. Our proofs do not require restrictions on direction of approach, so we recover new information on the locus in the moduli space of curves on which the maximal rank condition fails.References
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Additional Information
- Fu Liu
- Affiliation: Department of Mathematics, University of California Davis, One Shields Avenue, Davis, California 95616
- ORCID: 0000-0003-0497-4083
- Email: fuliu@math.ucdavis.edu
- Brian Osserman
- Affiliation: Department of Mathematics, University of California Davis, One Shields Avenue, Davis, California 95616
- MR Author ID: 722512
- Montserrat Teixidor i Bigas
- Affiliation: Department of Mathematics, Tufts University, Medford, Massachusetts 02155
- MR Author ID: 214136
- Email: mteixido@tufts.edu
- Naizhen Zhang
- Affiliation: Institut für Differentialgeometrie, Gottfried Wilhelm Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover, Germany
- MR Author ID: 907245
- Email: naizhen.zhang@math.uni-hannover.de
- Received by editor(s): March 15, 2017
- Received by editor(s) in revised form: April 22, 2020
- Published electronically: November 2, 2020
- Additional Notes: The first author was partially supported by NSF grant DMS-1265702.
The second author was partially supported by a grant from the Simons Foundation #279151. - © Copyright 2020 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 374 (2021), 367-405
- MSC (2010): Primary 14D06, 14H51
- DOI: https://doi.org/10.1090/tran/8230
- MathSciNet review: 4188187