Co-Higgs bundles on P^1

Steven Rayan

Co-Higgs bundles on P¹

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arxiv 1010.2526 v2 pith:SZUKT3XG submitted 2010-10-12 math.AG math.DG

Co-Higgs bundles on P¹

Steven Rayan This is my paper

classification math.AG math.DG

keywords bundlebundleshiggsco-higgsadhmadmitbetticharacterize

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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.

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