Our proof confirms the Kodaira vanishing theorem for complex surfaces, highlighting counterexamples in positive characteristic.
We give a proof of the Kodaira vanishing theorem on smooth complex surfaces using geometric stability conditions. Likewise, we give a new proof of a result of Xie [Chinese Ann. Math. Ser. B 32 (2011), 741–748] characterizing the counterexamples of the Kodaira vanishing theorem on surfaces in positive characteristic.
No takes yet. Share an insight, caveat, or question.
Cristián Caamaño Martinez (2025) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: