Moduli Spaces and Vector Bundles: Geometric Invariant Theory

By Peter E. Newstead. 2009

1,227 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/e997e9d45d0ef3e66d5ef3240a75a3b9f23b137d

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In Geometry and Topology

Citations in the corpus

o-minimal GAGA and a conjecture of Griffiths (2018, result): “Let M be a separated Deligne–Mumford stack of finite type over C admitting a quasi-finite Ran,exp-definable period map, and let Z be a reduced algebraic space.”
Balanced line bundles and equivariant compactifications of homogeneous spaces (2013, background): “6 of [MFK94] implies that some multiple of Dα is G-linearizable.”
Positivity for quantum cluster algebras (2016, background): “[MFK94], the GIT quotient X(Q)d//χGd provides a coarse moduli space of ζsemistable d-dimensional right CQ-modules.”
Periods and harmonic analysis on spherical varieties (2012, background): “Recall that, when a reductive group acts on an affine variety, any two closed sets are separated by an invariant function (see [MFK94]).”
Uniform K-stability and asymptotics of energy functionals in Kähler geometry (2016, methodology): “4 is the following algebro-geometric result, which will be obtained as a consequence of the Iwahori decomposition theorem, very much as in [MFF].”
Néron models and compactified Picard schemes over the moduli stack of stable curves (2005, methodology): “The language and the techniques used in this paper are mostly those of [BLR] for the theory of Néron models, and of [GIT] for Geometric Invariant Theory and its applications to moduli problems.”
Introduction to actions of algebraic groups (2010, methodology): “We refer to the notes of Woodward for this and further developments; the books by Dolgachev (see [1]) and Mukai (see [8]) may also be recommended, as well as the classic by Mumford, Kirwan and Fogarty (see [9]).”
Hypersurfaces in projective schemes and a moving lemma (2014, background): “(a) This statement is well-known (it is found for instance in [52], page 20,”
Moduli of representations of quivers (2008, background): “We follow mainly the presentation of [48], since the generality of the standard text [47] is not used in the following.”
Compact moduli space of Kahler-Einstein Fano varieties (2014, neutral): “Then we get a contradiction from the general geometric invariant theory [Mum] since i(Qi) and Pi are both GIT polystable, while being the limits of sequences which parametrise the same polystable point.”