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Variations of geometric invariant quotients for pairs, a computational approach


Authors: Patricio Gallardo and Jesus Martinez-Garcia
Journal: Proc. Amer. Math. Soc. 146 (2018), 2395-2408
MSC (2010): Primary 14L24, 14H10, 14Q10; Secondary 14J45, 14J32
DOI: https://doi.org/10.1090/proc/13950
Published electronically: February 16, 2018
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Abstract: We study GIT compactifications of pairs formed by a hypersurface and a hyperplane. We provide a general setting to characterize all polarizations which give rise to different GIT quotients. Furthermore, we describe a finite set of one-parameter subgroups sufficient to determine the stability of any GIT quotient. We characterize all maximal orbits of non-stable and strictly semistable pairs, as well as minimal closed orbits of strictly semistable pairs. Our construction gives natural compactifications of the space of log smooth pairs for Fano and Calabi-Yau hypersurfaces.


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Additional Information

Patricio Gallardo
Affiliation: Department of Mathematics, Washington University, Campus Box 1146, One Brookings Drive, St. Louis, Missouri 63130-4899
Email: pgallardocandela@wustl.edu

Jesus Martinez-Garcia
Affiliation: Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, United Kingdom
Email: J.Martinez.Garcia@bath.ac.uk

DOI: https://doi.org/10.1090/proc/13950
Received by editor(s): March 29, 2016
Received by editor(s) in revised form: September 7, 2017
Published electronically: February 16, 2018
Communicated by: Lev Borisor
Article copyright: © Copyright 2018 American Mathematical Society

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