Some quadratic inequalities on product varieties

2020/10/27 by Yucheng Liu, Liu, Yucheng · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #FOS: Mathematics #Nonlinear Waves and Solitons #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2010.14039

openalex publication_date 2020/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove some positivity results on the coefficients in the complexified Hilbert polynomial of a semi-stable object. After applying these results on the classical slope stability conditions, we get sequences of quadratic inequalities for semi-stable objects on product varieties. The leading quadratic inequality can be viewed as a weak version of Bogomolov's inequality holding in arbitrary characteristics.

Citations

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Stability conditions on product varieties

Cited by

• Bogomolov type inequalities and Frobenius semipositivity

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