Log pluricanonical representations and abundance conjecture

By O. Fujino, Yoshinori Gongyo. 2011

69 citations recorded by the source corpus.

We prove the finiteness of log pluricanonical representations for projective log canonical pairs with semi-ample log canonical divisor. As a corollary, we obtain that the log canonical divisor of a projective semi log canonical pair is semi-ample if and only if so is the log canonical divisor of its normalization. We also treat many other applications.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5f748f3e8e849034263be46a72c8f66c8a3ca90c

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In Geometry and Topology

1. C. Birkar
2. Y. Odaka
3. Christopher D. Hacon
4. H. Blum
5. O. Fujino
6. F. Catanese
7. Ingrid Bauer
8. Stefano Filipazzi

In Mathematical Physics

1. C. Birkar
2. Christopher D. Hacon
3. Stefano Filipazzi

Citations in the corpus

• Boundedness of moduli of varieties of general type (2014, unknown): “See [15], [3], [8], [7], [9] and [14, 4.”
• Existence of log canonical flips and a special LMMP (2011, background): “divisor KX +Bto semi-ampleness in the klt case (cf. [22]). It is a consequence of Koll´ar’s injectivity theorem and semi-ampleness on semi-lc pairs. When Zis projective, it follows from Fujino-Gongyo [15]; the general case was proved by Hacon and Xu [20]. Theorem 1.7 ([15], [20]). Let (X/Z,B) be a Q”