Equality of the Wobbly and Shaky Loci

  1. Peón-Nieto, Ana 12
  1. 1 Department of Mathematics, Universidade de Santiago de Compostela , Rúa de Lope Gómez de Marzoa, s/n, 15705 Santiago de Compostela, A Coruña, Spain
  2. 2 School of Mathematics, University of Birmingham, Watson Building , Edgebaston, Birmingham B15 2TT, UK
Journal:
International Mathematics Research Notices

ISSN: 1073-7928,  1687-0247

Year of publication: 2023

Volume: 2024

Issue: 8

Pages: 6710-6730

Type: Article

DOI: 10.1093/IMRN/RNAD254 GOOGLE SCHOLAR lock_openOpen access editor

More publications in: International Mathematics Research Notices

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 E on X is (strongly) wobbly, that is, E 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. © The Author(s) 2023.

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