Co-Higgs bundles on P^1

Details Co-Higgs bundles on P^1 Co-Higgs bundles on P^1

2010-10-12

arxiv.org/abs/1010.2526v1

Mathematics

Algebraic Geometry

9 pages

Scientific paper

Co-Higgs bundles are Higgs bundles in the sense of Simpson, but with Higgs fields that take values in the tangent bundle instead of the cotangent bundle. Given a vector bundle on P^1, we find necessary and sufficient conditions on its Grothendieck splitting for it to admit a stable Higgs field. We characterize the rank-2, odd-degree moduli space as a universal elliptic curve with a globally-defined equation.

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