CO-HIGGS BUNDLES ON P 1

By S. Rayan. 2010

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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. For ranks r=2,3,4, we explicitly verify the conjectural Betti numbers emerging from the recent work of Chuang, Diaconescu, Pan, and Mozgovoy on the ADHM formula. We state the result for r=5.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/103c991607cfe1feb54fca0dff8f249fc72abfd5