The GIT-stability of Polarised Varieties via discrepancy

By Y. Odaka. 2008

126 citations recorded by the source corpus.

We prove that various GIT semistabilities of polarized varieties imply semi-log-canonicity.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f59aa27e92db127f3b97dc6556d1abaadd636e38

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Fundamental theorems for semi log canonical pairs (2012, background): “KSB] is not directly related to Mumford’s geometric invariant theory. However, the notion of semi log canonical singularities appears to be natural from the geometric invariant theoretic viewpoint by [O]. Moreover, semi log canonical pairs play crucial roles in our inductive treatment of the log abu”
On the moduli of Kähler-Einstein Fano manifolds (2012, methodology): “of moduli as varieties or algebraic spaces. Personally speaking, the author’s original motivation for this program of constructing moduli is from his algebro-geometric observations on the K-stability [Od08], [Od11], which connected geometrically compactiﬁed moduli variety of general type varieties o”
On the proper moduli spaces of smoothable Kähler–Einstein Fano varieties (2014, background): “Apart from some local properties, for example, having only Kawamata log terminal (klt) singularities when a Fano variety is assumed to be K-semistable (see [36]) and admitting klt Fano degenerations as long as the general fiber is a klt Fano variety in a 1-parameter family (see [34]), it is still no”
Special test configurations and $K$-stability of Fano varieties (2011, methodology): “is a special example of the intersection formula. 16 2. This intersection formula is related to the interpretation of Donaldson-Futaki invariant as the CM-weight in [PT06]. It was extensively used in [Oda08], [RT07], etc. 3. When (Xtc,Ltc) → A1 is a test conﬁguration, where we only assume Ltc to be ”
K-polystability of Q-Fano varieties admitting Kähler-Einstein metrics (2012, background): “riking feature of the Fano setting is that it is enough to consider normal varieties and even those with “mild singularities” in the sense of the Minimal Model Program in birational geometry (compare [28, 22]) . Note also that the case of a Fano varieties with quotient singularities, i.e. Xis a Fano”
Uniform K-stability, Duistermaat-Heckman measures and singularities of pairs (2015, methodology): “mple test conguration (X;L). In the klt case, there automatically exists >0 such that HNA B (X;L) JNA(X;L) for all (X;L). The strategy to prove the rst two points is closely related to that of [Oda13b]. In fact, we also provide a complete proof of the following mild generalization (in the normal ”
Uniform stability of twisted constant scalar curvature K\"ahler metrics (2014, background): “By Odaka-Sun [31, Corollary 3.6], to check log K-stability, it is equivalent to show that DFlog(B,L r − E,D) > 0 for all flag ideals with Lr − E relatively semi-ample over P1.”
Compact Moduli Spaces of Del Pezzo Surfaces and K\"ahler-Einstein metrics (2012, result): “the existence of a Kahler-Einstein metric implies K-polystability [9]. It turns out that the notion of K-stability is also closely related with the singularities allowed in the KSBA compactiﬁcations ([49], [50]): for varieties with ample canonical class, the notion of K-stability coincides with the ”