Author:
Boggi Marco,Looijenga Eduard
Abstract
AbstractLet 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
;
Q
)
and with image a $${{\mathbb {Q}}}$$
Q
-almost simple group.
Funder
National Natural Science Foundation of China
CNPq
Publisher
Springer Science and Business Media LLC
Reference25 articles.
1. André, Y.: Mumford-Tate groups of mixed Hodge structures and the theorem of the fixed part. Compos. Math. 82, 1–24 (1992)
2. Boggi, M., Looijenga, E.: Deforming a canonical curve inside a quadric. Int. Math. Res. Not. IMRN, https://doi.org/10.1093/imrn/rny027 (2018)
3. Chevalley, C., Weil, A., Hecke, E.: Über das Verhalten der Integrale 1. Gattung bei Automorphismen des Funktionenkörpers. Abh. Math. Sem. Univ. Hamburg 10, 358–361 (1934)
4. Ciliberto, C.: Endomorfismi di Jacobiane. Rend. Sem. Mat. Fis. Milano 59, 213–242 (1989)
5. Ciliberto, C., van der Geer, G., Teixidor i Bigas, M.: On the number of parameters of curves whose Jacobians possess nontrivial endomorphisms. J. Algebra. Geom. 1, 215–229 (1992)
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献