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EnglishIn a previous paper, arXiv:1206.5498, we introduced a new homological invariant $\e$ for the faithful action of a finite group G on an algebraic curve. We show here that the moduli space of curves admitting a faithful action of a finite group G with a fixed homological invariant $\e$, if the genus g' of the quotient curve is sufficiently large, is irreducible (and non empty iff the class satisfies the condition which we define as 'admissibility'). In the unramified case, a similar result had been proven by Dunfield and Thurston using the classical invariant in the second homology group of G, H_2(G, \ZZ). We achieve our result showing that the stable classes are in bijection with the set of admissible classes $\e$.
| Titolo: | Genus stabilization for the components of moduli spaces of curves with symmetries |
| Autori: | |
| Data di pubblicazione: | 2016 |
| Rivista: | |
| Abstract: | In a previous paper, arXiv:1206.5498, we introduced a new homological invariant $\e$ for the faithful action of a finite group G on an algebraic curve. We show here that the moduli space of curves admitting a faithful action of a finite group G with a fixed homological invariant $\e$, if the genus g' of the quotient curve is sufficiently large, is irreducible (and non empty iff the class satisfies the condition which we define as 'admissibility'). In the unramified case, a similar result had been proven by Dunfield and Thurston using the classical invariant in the second homology group of G, H_2(G, \ZZ). We achieve our result showing that the stable classes are in bijection with the set of admissible classes $\e$. |
| Handle: | http://hdl.handle.net/11368/2840449 |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.14231/AG-2016-002 |
| URL: | http://algebraicgeometry.nl/2016-1/2016-1-002.pdf |
| Appare nelle tipologie: | 1.1 Articolo in Rivista |
File in questo prodotto:
| File | Descrizione | Tipologia | Licenza | |
|---|---|---|---|---|
| CLP_AG_2016.pdf | Articolo principale | Documento in Versione Editoriale |  | Open Access Visualizza/Apri |
http://hdl.handle.net/11368/2840449
