Suppose that $C$ is a complex riemann surface of positive genus lying in a complex algebraic surface of general type. Let $T_C$ the tangent bundle to the curve $C$. Is there a way to compute the cohomology of this bundle?
i.e. the spaces $H^i(C,T_C)$ for $i=0,1$?
2026-03-30 23:17:17.1774912637
cohomology of a tangent bundle
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