Criteria for existence of stable parahoric $\SO_n$, $\Sp_n$ and $\Spin$ bundles on $\PP^1$

Yashonidhi Pandey

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arXiv · 1202.1897

Criteria for existence of stable parahoric $\SO_n$, $\Sp_n$ and $\Spin$ bundles on $\PP^1$

Yashonidhi Pandey

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Abstract

Let $p: Y \ra X$ be a Galois cover of smooth projective curves over $\CC$ with Galois group $\Gamma$. This paper is devoted to the study of principal orthogonal and symplectic bundles $E$ on $Y$ to which the action of $\Gamma$ 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 $\PP^1$.

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BibTeX RIS

Yashonidhi Pandey. 2012-02-09. Criteria for existence of stable parahoric $\SO_n$, $\Sp_n$ and $\Spin$ bundles on $\PP^1$. https://arxiv.org/abs/1202.1897

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