Variations of geometric invariant quotients for pairs, a computational approach
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- by Patricio Gallardo and Jesus Martinez-Garcia
- Proc. Amer. Math. Soc. 146 (2018), 2395-2408
- 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.References
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Bibliographic Information
- Patricio Gallardo
- Affiliation: Department of Mathematics, Washington University, Campus Box 1146, One Brookings Drive, St. Louis, Missouri 63130-4899
- MR Author ID: 1228133
- Email: pgallardocandela@wustl.edu
- Jesus Martinez-Garcia
- Affiliation: Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, United Kingdom
- MR Author ID: 1073616
- Email: J.Martinez.Garcia@bath.ac.uk
- 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
- © Copyright 2018 American Mathematical Society
- 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
- MathSciNet review: 3778143