Equality of the wobbly and shaky loci

Ana Peon-Nieto*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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Abstract

Let X be a smooth complex projective curve of genus g ≥ 2, and let D ⊂ X be a reduced divisor. We prove that a parabolic vector bundle ℇ on X is (strongly) wobbly, that is, ℇ has a non-zero (strongly) parabolic nilpotent Higgs field, if and only if it is (strongly) shaky, that is, it is in the image of the exceptional divisor of a suitable resolution of the rational map from the (strongly) parabolic Higgs moduli to the vector bundle moduli space, both assumed to be smooth. This solves a conjecture by Donagi–Pantev [ 14] in the parabolic and the vector bundle context. To this end, we prove the stability of strongly very stable parabolic bundles, and criteria for very stability of parabolic bundles.
Original languageEnglish
Article numberrnad254
Pages (from-to)1-21
Number of pages21
JournalInternational Mathematics Research Notices
Early online date8 Nov 2023
DOIs
Publication statusE-pub ahead of print - 8 Nov 2023

Bibliographical note

Funding:
This work was supported by the European Union-AGAUR under the scheme Beatriu de Pinós-H2020-MSCA-COFUND-2017 (agreement n. 801370), the European Union, scheme H2020-MSCA-IF-2019 (agreement n. 897722), and the Agencia Estatal de Investigación, scheme Consolidación Investigadora (grant no. CNS2022-136042).

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