 

Steven Rayan
CoHiggs bundles on P^{1} view print


Published: 
November 27, 2013 
Keywords: 
CoHiggs bundle, Higgs bundle, Hitchin fibration, projective line, stability, moduli space, Betti numbers, holomorphic chain 
Subject: 
14D20, 14H60, 14D22 


Abstract
CoHiggs 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 rank2, odddegree moduli space as a universal elliptic curve with a globallydefined 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.


Acknowledgements
Parts of this work were funded by the Commonwealth Scholarship Plan and the Natural Sciences & Engineering Research Council of Canada.


Author information
Dept. of Mathematics, Univ. of Toronto, 40 St. George St., Toronto, ON, CANADA, M5S 2E4.
rayan@math.toronto.edu

