Variations of geometric invariant quotients for pairs, a computational approach

Patricio Gallardo, Jesus Martinez-Garcia

Research output: Contribution to journalArticle

3 Citations (Scopus)
27 Downloads (Pure)

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.

Original languageEnglish
Pages (from-to)2395-2408
Number of pages14
JournalProceedings of the American Mathematical Society
Volume146
Issue number6
Early online date16 Feb 2018
DOIs
Publication statusPublished - 2018

Fingerprint

Geometric Invariants
Quotient
Orbits
Compactification
Hypersurface
Strictly
Polarization
Closed Orbit
Calabi-Yau
Hyperplane
Finite Set
Orbit
Subgroup
Sufficient

ASJC Scopus subject areas

  • Geometry and Topology
  • Algebra and Number Theory

Cite this

Variations of geometric invariant quotients for pairs, a computational approach. / Gallardo, Patricio; Martinez-Garcia, Jesus.

In: Proceedings of the American Mathematical Society, Vol. 146, No. 6, 2018, p. 2395-2408 .

Research output: Contribution to journalArticle

Gallardo, Patricio ; Martinez-Garcia, Jesus. / Variations of geometric invariant quotients for pairs, a computational approach. In: Proceedings of the American Mathematical Society. 2018 ; Vol. 146, No. 6. pp. 2395-2408 .
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