 

Yuxiang Ji
Small angle limits of negatively curved KahlerEinstein metrics with crossing edge singularities
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Published: 
April 15, 2024. 
Keywords: 
KahlerEinstein edge metrics,
Poincare singularities, holomorphic bisectional curvature. 
Subject [2010]: 
32Q20, 53C21. 


Abstract
Let (X,D) be a log smooth log canonical pair such that K_{X}+D is ample. Extending a theorem of Guenancia and building on his techniques, we show that negatively curved KahlerEinstein crossing edge metrics converge to KahlerEinstein mixed cusp and edge metrics smoothly away from the divisor when some of the cone angles converge to 0. We further show that near the divisor such normalized KahlerEinstein crossing edge metrics converge to a mixed cylinder and edge metric in the pointed GromovHausdorff sense when some of the cone angles converge to 0 at (possibly) different speeds.


Acknowledgements
Research supported in part by the NSF grant DMS1906370 and the Michael Brin Graduate Fellowship at the University of Maryland.


Author information
Yuxiang Ji
Department of Mathematics
University of Maryland
College Park, MD 20740, USA
yxji@umd.edu

