Prym-Tyurin varieties via Hecke algebras

Details Prym-Tyurin varieties via Hecke algebras Prym-Tyurin varieties via Hecke algebras

2008-05-29

arxiv.org/abs/0805.4563v2

Mathematics

Algebraic Geometry

24 pages. Accepted in J. Reine Angew. Math. Minor changes

Scientific paper

Let $G$ denote a finite group and $\pi: Z \to Y$ a Galois covering of smooth projective curves with Galois group $G$. For every subgroup $H$ of $G$ there is a canonical action of the corresponding Hecke algebra $\mathbb{Q}[H \backslash G/H]$ on the Jacobian of the curve $X = Z/H$. To each rational irreducible representation $\mathcal{W}$ of $G$ we associate an idempotent in the Hecke algebra, which induces a correspondence of the curve $X$ and thus an abelian subvariety $P$ of the Jacobian $JX$. We give sufficient conditions on $\mathcal{W}$, $H$, and the action of $G$ on $Z$, which imply $P$ to be a Prym-Tyurin variety. We obtain many new families of Prym-Tyurin varieties of arbitrary exponent in this way.

Affiliated with

Also associated with

No associations

Rating

Prym-Tyurin varieties via Hecke algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Prym-Tyurin varieties via Hecke algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Prym-Tyurin varieties via Hecke algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-179760