A 2-systolic inequality on non-rational compact K\"ahler surfaces with positive scalar curvature

Zehao Sha

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arXiv · 2510.13353

A 2-systolic inequality on non-rational compact K\"ahler surfaces with positive scalar curvature

Zehao Sha

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Abstract

In this note, we prove a 2-systolic inequality on compact positive scalar curvature K\"ahler surfaces admitting a nonconstant holomorphic map to a positive-genus compact Riemann surface. According to the classification of positive scalar curvature K\"ahler surfaces, any such surface must be a ruled surface fibred over a complex curve with positive genus.

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Zehao Sha. 2025-10-15. A 2-systolic inequality on non-rational compact K\"ahler surfaces with positive scalar curvature. https://arxiv.org/abs/2510.13353

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