Journal article
Holomorphic differentials of Klein four covers
Journal of pure and applied algebra, Vol.227(10), 107384
10/2023
DOI: 10.1016/j.jpaa.2023.107384
Abstract
Let k be an algebraically closed field of characteristic two, and let G be isomorphic to Z/2×Z/2. Suppose X is a smooth projective irreducible curve over k with a faithful G-action, and assume that the cover X→X/G is totally ramified, in the sense that it is ramified and every branch point is totally ramified. We study to what extent the lower ramification groups of the closed points of X determine the isomorphism types of the indecomposable kG-modules and the multiplicities with which they occur as direct summands of the space H0(X,ΩX/k) of holomorphic differentials of X over k. In the case when X/G=Pk1, we completely determine the decomposition of H0(X,ΩX/k) into a direct sum of indecomposable kG-modules. Moreover, we show that the isomorphism classes of indecomposable kG-modules that actually occur as direct summands belong to an infinite list of non-isomorphic indecomposable kG-modules that contain modules of arbitrarily large k-dimension. In particular, our results show that [14, Theorem 6.4] is incorrect.
Details
- Title: Subtitle
- Holomorphic differentials of Klein four covers
- Creators
- Frauke M. BleherNicholas Camacho
- Resource Type
- Journal article
- Publication Details
- Journal of pure and applied algebra, Vol.227(10), 107384
- DOI
- 10.1016/j.jpaa.2023.107384
- ISSN
- 0022-4049
- eISSN
- 1873-1376
- Publisher
- Elsevier B.V
- Grant note
- DMS-1801328 / NSF (https://doi.org/10.13039/100000001)
- Language
- English
- Date published
- 10/2023
- Academic Unit
- Mathematics
- Record Identifier
- 9984388759702771
Metrics
25 Record Views