2006/12/19 by Yujen Shu, Shu, Yujen · 1 citation
Mathematics · Physics and Astronomy · #14Q10 #53C25 #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.math/0612571
openalex publication_date 2006/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Being inspired by Ross' construction of unstable products of certain smooth curves, we show that the product C× C of every smooth curve C of genus at least 2 is not slope semistable with respect to certain polarisations. Besides, we produce examples of Kodaira-fibred surfaces of nonzero signature, which are not slope semistable with respect to some polarisations, and so they admit Kähler classes that do not contain any constant scalar curvature Kähler metrics.