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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.26044 |
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Table of Contents:
- Splitting loci are certain natural closed substacks of the stack of vector bundles on $\mathbb{P}^1$, which have found interesting applications in the Brill-Noether theory of $k$-gonal curves. In this paper, we completely characterize when splitting loci, as algebraic stacks, are Gorenstein or $\mathbb{Q}$-Gorenstein. The main ingredients of the proof are a computation of the class groups of splitting loci in certain affine extension spaces, and a formula for the class of their canonical module.