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Curves with prescribed symmetry and associated representations of mapping class groups
- Source :
- Mathematische Annalen, 381(3-4), 1511. Springer New York
- Publication Year :
- 2021
-
Abstract
- Let C be a complex smooth projective algebraic curve endowed with an action of a finite group G such that the quotient curve has genus at least 3. We prove that if the G-curve C is very general for these properties, then the natural map from the group algebra $${{\mathbb {Q}}}G$$ Q G to the algebra of $${{\mathbb {Q}}}$$ Q -endomorphisms of its Jacobian is an isomorphism. We use this to obtain (topological) properties regarding certain virtual linear representations of a mapping class group. For example, we show that the connected component of the Zariski closure of such a representation often acts $${{\mathbb {Q}}}$$ Q -irreducibly in a G-isogeny space of $$H^1(C; {{\mathbb {Q}}})$$ H 1 ( C Íž Q ) and with image a $${{\mathbb {Q}}}$$ Q -almost simple group.
- Subjects :
- Finite group
Mathematics(all)
Endomorphism
General Mathematics
Image (category theory)
010102 general mathematics
Group algebra
01 natural sciences
Mapping class group
Combinatorics
0103 physical sciences
010307 mathematical physics
Algebraic curve
Isomorphism
0101 mathematics
Quotient
Mathematics
Subjects
Details
- Language :
- English
- ISSN :
- 00255831
- Database :
- OpenAIRE
- Journal :
- Mathematische Annalen, 381(3-4), 1511. Springer New York
- Accession number :
- edsair.doi.dedup.....b897b1a4fe372904e6c4563230bef496