Minimal Model Theory for Log Surfaces

By O. Fujino. 2010

87 citations recorded by the source corpus.

We discuss the log minimal model program for log surfaces. We show that the minimal model program for surfaces works under much weaker assumptions than we expected.

Subfields: Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/5ff25960e2bae862808e614cdc88755973321573

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In Geometry and Topology

Citations in the corpus

Fundamental Theorems for the Log Minimal Model Program (2009, background): “es. In [F13], we prove the ﬁnite generation of the log canonical ring for log canonical pairs in dimension four and discuss related topics. It induces the existence of fourfold log canonical ﬂips. In [F17], we discuss the minimal model theory for log surfaces. The results in [F17] are obtained under”
A TRANSCENDENTAL APPROACH TO KOLL AR'S INJECTIVITY THEOREM II (2007, methodology): “We have already obtained many applications for the log minimal model program in [17], [19], [13], [14], [15], [22], [16], [18], and [20].”
Fundamental theorems for semi log canonical pairs (2012, methodology): “ier because C is not Q-Cartier on X. Therefore, we can not always run the minimal model program for semi log canonical surfaces. For a new framework of the minimal model program for log surfaces, see [F13], [FT], [T1], and [T2]. 6. Miscellaneous applications In this paper, we adopt the following deﬁ”
Log pluricanonical representations and abundance conjecture (2011, unknown): “ and that KX+∆ is semi-ample. Then ρm(Bir(X,∆)) is a ﬁnite group. In the framework of [F1], Theorem 1.1 will play important roles in the study of Conjecture 1.2 (see [Ft], [AFKM], [Ka2], [KMM], [F1], [F8], [G2], and so on). Conjecture 1.2 ((Log) abundance conjecture). Let (X,∆) be a projective semi ”