“Log Abundance Theorem for Threefolds ” by Sean Keel, Kenji Matsuki, and

Abundance Theorem for Semi Log Canonical Threefolds

for semi log canonical threefolds. The abundance conjecture is a very important problem in the birational classi cation of algebraic varieties. The abundance theorem for semi log canonical surfaces was proved in [12, Chapter 8, 12] by L.-Y. Fong, S. Keel, J. Koll ar, and J. McKernan. Their proof uses semiresolution, etc. and has some combinatorial complexities. So we simplify their proof and st...

Erratum to the Paper “a Note on the Factorization Theorem of Toric Birational Maps after Morelli and Its Toroidal Extension”

1. the failure of the algorithm in [AMR] and [Morelli1] for the strong factorization pointed out by Kalle Karu, 2. the statement of a refined weak factorization theorem for toroidal birational morphisms in [AMR], in the form utilized in [AKMR] for the proof of the weak factorization theorem for general birationla maps, avoiding the use of the above mentioned algorithm for the strong factorizati...

4 Ju n 20 11 MIRROR SYMMETRY FOR LOG CALABI - YAU SURFACES I

Boundedness theorem for Fano log-threefolds

The main purpose of this article is to prove that the family of all Fano threefolds with log-terminal singularities with bounded index is bounded.

The Cone of Effective Divisors of Log Varieties after Batyrev

In [Bat92] Batyrev studied the cone of pseudo-effective divisors on Q-factorial terminal threefolds and its dual cone, the cone of nef curves. Given a uniruled Q-factorial terminal threefold X , and an ample divisor H on X , he showed that the effective threshold of H (see Definition 1.5 below) is a rational number. Using similar arguments, Fujita generalized this result to log terminal pairs (...