Decomposing Representations of Finite Groups on Riemann-roch Spaces
نویسندگان
چکیده
If G is a finite subgroup of the automorphism group of a projective curve X and D is a divisor on X stabilized by G, then we compute a simplified formula for the trace of the natural representation of G on the Riemann-Roch space L(D), under the assumption that L(D) is “rational”, D is nonspecial, and the characteristic is “good”. We discuss the partial formulas that result if L(D) is not rational.
منابع مشابه
N ov 2 00 2 Representations of finite groups on Riemann - Roch spaces
We study the action of a finite group on the Riemann-Roch space of certain divisors on a curve. If G is a finite subgroup of the automor-phism group of a projective curve X and D is a divisor on X stable by G then we show the natural representation of G on Riemann-Roch space L(D) = L X (D) is a direct sum of irreducible representations of dimension ≤ d, where d is the size of the smallest G-orb...
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If G is a finite subgroup of the automorphism group of a projective curve X and D is a divisor on X stabilized by G, then under the assumption that D is nonspecial, we compute a simplified formula for the trace of the natural representation of G on Riemann-Roch space L(D).
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