Families of cyclic curve coverings with maximal monodromy
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912905687990272 |
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| author | Spelta, Irene Tamborini, Carolina |
| author_facet | Spelta, Irene Tamborini, Carolina |
| contents | We study the algebraic monodromy of families of cyclic Galois coverings of curves. Under a condition on the $G$-decomposition of the associated variation of Hodge structures, we prove a criterion for the maximality of the monodromy. The proof combines the genus-zero case with a degeneration argument involving Prym varieties of certain admissible coverings. As a consequence of our criterion, we show that for $g\geq 8$ there exists no special family of Galois covers of the type we consider, providing new evidence towards the Coleman-Oort conjecture. Finally, we determine when the loci of double and triple Galois covers are totally geodesic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_23479 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Families of cyclic curve coverings with maximal monodromy Spelta, Irene Tamborini, Carolina Algebraic Geometry 14H10, 14H40, 14G35, 14D07 We study the algebraic monodromy of families of cyclic Galois coverings of curves. Under a condition on the $G$-decomposition of the associated variation of Hodge structures, we prove a criterion for the maximality of the monodromy. The proof combines the genus-zero case with a degeneration argument involving Prym varieties of certain admissible coverings. As a consequence of our criterion, we show that for $g\geq 8$ there exists no special family of Galois covers of the type we consider, providing new evidence towards the Coleman-Oort conjecture. Finally, we determine when the loci of double and triple Galois covers are totally geodesic. |
| title | Families of cyclic curve coverings with maximal monodromy |
| topic | Algebraic Geometry 14H10, 14H40, 14G35, 14D07 |
| url | https://arxiv.org/abs/2512.23479 |