An Introduction to Invariants and Moduli

By S. Mukai. 2003

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Topology of character varieties of Abelian groups (2013, background): “See [12] or [34] for the details of these constructions and an introduction to GIT.”
Moduli of representations of quivers (2008, methodology): “We recall the basic concepts of Geometric Invariant Theory as in [48], and use them to construct the moduli spaces of stable representations, following [37], in section 3.”
Sagbi Bases of Cox-Nagata Rings (2008, methodology): “See [23, §12.5].”
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]).”
Some remarks on Brauer groups of K3 surfaces (2004, methodology): “nd we recover the associated Jacobian ﬁbration f : X → P1. For this we only use the classical construction of the Jacobian of a double cover of P1 branched over four points, due to Hermite (cf. [We], [Mu3]), i.e. we consider the generic ﬁbers of g and f over the ﬁeld k(P1). This construction also gi”
Localization in quiver moduli spaces (2009, background): “For a detailed description of the theory of quotients see [20].”