A note on stability of syzygy bundles on Enriques and bielliptic surfaces
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- by Jayan Mukherjee and Debaditya Raychaudhury PDF
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Abstract:
In this note, we prove that the syzygy bundle $M_L$ is cohomologically stable with respect to $L$ for any ample and globally generated line bundle $L$ on an Enriques (resp. bielliptic) surface over an algebraically closed field of characteristic $\neq 2$ (resp. $\neq 2,3$). In particular our result on complex Enriques surfaces improves the result of Torres-López and Zamora [Beitr. Algebra Geom. (2021)] (Corollary 3.5) by removing the condition on Clifford index. Together with the results of Camere [Math. Z 271 (2012), pp. 499–507] and Caucci–Lahoz [Bull. Lond. Math. Soc. 53 (2021), pp. 1030–1036], it implies that $M_L$ is stable with respect to $L$ for an ample and globally generated line bundle $L$ on any smooth minimal complex projective surface $X$ of Kodaira dimension zero.References
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Additional Information
- Jayan Mukherjee
- Affiliation: The Institute for Computational and Experimental Research in Mathematics, Providence, Rhode Island 02903
- MR Author ID: 1339173
- Email: jayan_mukherjee@brown.edu
- Debaditya Raychaudhury
- Affiliation: The Fields Institute for Research in Mathematical Sciences, Toronto, Canada
- MR Author ID: 1339282
- Email: draychau@fields.utoronto.ca
- Received by editor(s): September 8, 2021
- Received by editor(s) in revised form: November 17, 2021
- Published electronically: June 3, 2022
- Additional Notes: The first author was supported by the National Science Foundation, Grant No. DMS-1929284 while in residence at the Institute for Computational and Experimental Research in Mathematics in Providence, RI, as part of the ICERM Bridge program.
The research of the second author was supported by a Simons Postdoctoral Fellowship from the Fields Institute for Research in Mathematical Sciences. - Communicated by: Claudia Polini
- © Copyright 2022 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 150 (2022), 3715-3724
- MSC (2020): Primary 14J27, 14J28, 14J60
- DOI: https://doi.org/10.1090/proc/15934
- MathSciNet review: 4446224