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 language | English |
|---|---|
| Article number | rnad254 |
| Pages (from-to) | 1-21 |
| Number of pages | 21 |
| Journal | International Mathematics Research Notices |
| Early online date | 8 Nov 2023 |
| DOIs | |
| Publication status | E-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).