Which powers of holomorphic functions are integrable?
J\'anos Koll\'ar (Princeton Univ)
TL;DR
This paper investigates the properties of holomorphic functions and their integrability by examining the limits of log canonical thresholds across different dimensions, revealing a dimensional reduction in these thresholds.
Contribution
It demonstrates that limits of log canonical thresholds in n variables are also attainable as thresholds in (n-1) variables, establishing a new connection between thresholds across dimensions.
Findings
Limits of log canonical thresholds in n variables are also thresholds in (n-1) variables.
Establishes a dimensional reduction property for log canonical thresholds.
Provides insights into the integrability properties of holomorphic functions.
Abstract
We show that every limit of log canonical thresholds of n-variable functions is also a log canonical threshold of an (n-1)-variable function.
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Taxonomy
TopicsGeometry and complex manifolds · Algebraic Geometry and Number Theory · Meromorphic and Entire Functions