Mejía, Israel Moreno (2003) Representations of the space of n-theta functions. Doctoral thesis, Durham University.
Let X be a smooth complex projective curve with group of automorphisms G. In this thesis we apply the Holomorphic Lefschetz Theorem in certain cases to compute the decomposition of the space H (J(_x),O(_n)O)) into a sum of irreducible representations of G, where J(_x) is the Jacobian variety of X and O(O) is the theta line bundle of J(_x). Namely we compute this decomposition in the cases when X is the Klein quartic curve, the Bring curve of genus 4 and the Macbeath curve of genus 7.
|Item Type:||Thesis (Doctoral)|
|Award:||Doctor of Philosophy|
|Copyright:||Copyright of this thesis is held by the author|
|Deposited On:||26 Jun 2012 15:20|