Positivity, singularities, and boundedness

2025/07/24 by Birkar, Caucher
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.18394

Abstract

In this short note we will explore some recent connections between positivity, singularities, and boundedness in various contexts focusing on birational geometry.

Citations

• Singularities on Fano fibrations and beyond
• Boundedness and volume of generalised pairs
• Geometry of polarised varieties
• Singularities of linear systems and boundedness of Fano varieties
• Anti-pluricanonical systems on Fano varieties
• Singularities on the base of a Fano type fibration
• ACC for log canonical thresholds
• Existence of minimal models for varieties of log general type

Related

• Mini-Workshop: Positivity and Inequalities in Convex and Complex Geometry
• An infinite family of counterexamples to a conjecture on positivity
• What is Positive Geometry?
• Positivity for Hodge modules and geometric applications
• From Hörmander's L²-estimates to partial positivity