Parahoric Special Orthogonal, Symplectic and Spin Bundles on a compact Riemann surface -I

Details Parahoric Special Orthogonal, Symplectic and Spin Bundles on a compact Riemann surface -I Parahoric Special Orthogonal, Symplectic and Spin Bundles on a compact Riemann surface -I

2012-02-09

arxiv.org/abs/1202.1897v1

Mathematics

Algebraic Geometry

34 pages

Scientific paper

Let $p: Y \rightarrow X$ be a Galois cover of smooth projective curves over $\mathbb{C}$ with Galois group $\pi$. This paper is devoted to the study of principal orthogonal and symplectic bundles $E$ on $Y$ to which the action of $\pi$ on $Y$ lifts. We notably describe them intrinsically in terms of objects defined on $X$ and call these objects parahoric bundles. We give necessary and sufficient conditions for the non-emptiness of the moduli of stable and semi-stable parahoric special orthogonal, symplectic and spin bundles on the projective line $\mathbb{P}^1$.

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