On the positivity of the logarithmic cotangent bundle
Damian Brotbek (IRMA), Ya Deng (IRMA)
TL;DR
This paper constructs examples of smooth complex projective varieties with strongly positive logarithmic cotangent bundles by summing ample hypersurfaces, advancing understanding of positivity in algebraic geometry.
Contribution
It introduces a method to produce varieties with positively curved logarithmic cotangent bundles using ample hypersurfaces.
Findings
Examples of varieties with strongly positive logarithmic cotangent bundles
Method applicable to any smooth n-dimensional complex projective variety
Enhances understanding of positivity properties in algebraic geometry
Abstract
The aim of this work is to construct examples of pairs whose logarithmic cotangent bundles have strong positivity properties. These examples are constructed from any smooth n-dimensional complex projective varieties by considering the sum of at least n general sufficiently ample hypersurfaces.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Meromorphic and Entire Functions · Advanced Differential Equations and Dynamical Systems