Affiliation:
1. All Souls College University of Oxford Oxford UK
2. Mathematical Institute University of Oxford Oxford UK
Abstract
AbstractLet denote a rational cohomology class, and let denote its Hodge norm. We recover the result that is a plurisubharmonic function on the Teichmüller space , and characterize complex directions along which the complex Hessian of vanishes. Moreover, we find examples of such that is not strictly plurisubharmonic. As part of this construction, we find an unbranched covering such that the subgroup of generated by lifts of simple curves from is strictly contained in . Finally, combining the characterization theorem with the Riemann–Roch, and the Li–Yau [Invent. Math. 69 (1982), no. 2, 269–291] gonality estimate, we show that geometrically uniform covers of satisfy the Putman–Wieland Conjecture about the induced Higher Prym representations.
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