Infinitesimal extension of pluricanonical forms
Junyan Cao, Mihai Paun
TL;DR
This paper investigates the extension of pluricanonical forms in a smooth Kähler family, focusing on lifting twisted canonical sections from infinitesimal neighborhoods under L2 conditions.
Contribution
It provides new results on extending pluricanonical forms from infinitesimal neighborhoods in Kähler families, a novel contribution in complex geometry.
Findings
Lifting of twisted canonical sections verified under L2 conditions
First results on infinitesimal extension of pluricanonical forms in this context
Establishes foundational results for further studies in complex geometry
Abstract
The current paper represents the first part: it contains the results concerning the lifting of twisted canonical sections defined on an infinitesimal neighborhood of the central fiber of a smooth, proper K\"ahler family which verify a natural L2 condition.
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Taxonomy
TopicsGeometry and complex manifolds · Advanced Algebra and Geometry · Algebraic Geometry and Number Theory