Genus stabilization for the homology of moduli spaces of orbit-framed curves with symmetries-I
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910002378178560 |
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| author | Catanese, Fabrizio Loenne, Michael Perroni, Fabio |
| author_facet | Catanese, Fabrizio Loenne, Michael Perroni, Fabio |
| contents | In a previous paper, arXiv:1301.4409, we showed that the moduli space of curves C with a G-symmetry (that is, with a faithful action of a finite group G), having a fixed generalized homological invariant, is irreducible if the genus g' of the quotient curve C' : = C/G satisfies g'>>0.
Interpreting this result as stabilization for the 0-th homology group of the moduli space of curves with G-symmetry, we begin here a program for showing genus stabilization for all the homology groups of these spaces, in similarity to the results of Harer for the moduli space of curves.
In this first paper we prove homology stabilization for a variant of the moduli space where one G-orbit is tangentially framed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_10199 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Genus stabilization for the homology of moduli spaces of orbit-framed curves with symmetries-I Catanese, Fabrizio Loenne, Michael Perroni, Fabio Algebraic Geometry 14H15, 14H30, 14H37, 20J05, 30F60, 55M35, 57M12, 57S05 In a previous paper, arXiv:1301.4409, we showed that the moduli space of curves C with a G-symmetry (that is, with a faithful action of a finite group G), having a fixed generalized homological invariant, is irreducible if the genus g' of the quotient curve C' : = C/G satisfies g'>>0. Interpreting this result as stabilization for the 0-th homology group of the moduli space of curves with G-symmetry, we begin here a program for showing genus stabilization for all the homology groups of these spaces, in similarity to the results of Harer for the moduli space of curves. In this first paper we prove homology stabilization for a variant of the moduli space where one G-orbit is tangentially framed. |
| title | Genus stabilization for the homology of moduli spaces of orbit-framed curves with symmetries-I |
| topic | Algebraic Geometry 14H15, 14H30, 14H37, 20J05, 30F60, 55M35, 57M12, 57S05 |
| url | https://arxiv.org/abs/2508.10199 |