Log pluricanonical representations and the abundance conjecture

Abstract

Abstract. 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.

On minimal model theory for log abundant lc pairs

“…The class is very useful for inductive arguments on dimension of varieties. For example, the abundance conjecture for abundant klt pairs and log abundant lc pairs are studied by a lot of people ( [28], [37], [10], [19], [13], [17], [23]), and the conjecture is currently known in full generality ( [23], and [17] for projective case). In klt case, the existence of good minimal models or Mori fiber spaces is known ( [32] and [21]).…”

Basepoint-free theorems: saturation, b-divisors, and canonical bundle formula

“…(iii) The reader can find applications of this corollary in [Fukuda 2002;Fujino 2010;Fujino and Gongyo 2011].…”

“…We do not use the powerful new method developed in Fujino 2009a;2009b;2009c;2011b;2011c]. For related topics and applications, see [Fujino 2010;Gongyo 2010, Section 6;Cacciola 2011;Fujino and Gongyo 2011]. Remark 1.3.…”

Log canonical pairs over varieties with maximal Albanese dimension

“…We also need the following canonical bundle formula for lc-trivial fibrations from [1] or [22] as well.…”