The Morrison Cone Conjecture under Deformation
Wendelin Lutz
TL;DR
This paper demonstrates that the Morrison cone conjecture's validity for a smooth Calabi-Yau threefold extends to all deformation-equivalent threefolds, and applies this to establish a new case of the conjecture.
Contribution
It proves the invariance of the Morrison cone conjecture under deformation and establishes a new case of the conjecture for Calabi-Yau threefolds.
Findings
The Morrison cone conjecture is deformation-invariant.
A new case of the Morrison cone conjecture is proved.
The result applies to smooth Calabi-Yau threefolds.
Abstract
We prove that if the Morrison cone conjecture holds for a smooth Calabi-Yau threefold , it holds for any smooth Calabi-Yau threefold deformation-equivalent to . We use this result to prove a new case of the Morrison cone conjecture.
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Taxonomy
TopicsPoint processes and geometric inequalities · Computational Geometry and Mesh Generation · Mathematics and Applications