INTRODUCTION TO THE TORIC MORI THEORY
By O. Fujino, H. Sato. 2003
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The main purpose of this paper is to give a simple and non-combinatorial proof of the toric Mori theory. Here, the toric Mori theory means the (log) Minimal Model Program (MMP, for short) for toric varieties. We minimize the arguments on fans and their decompositions. We recommend this paper to the following people: (A) those who are uncomfortable with manipulating fans and their decompositions, (B) those who are familiar with toric geometry but not with the MMP. People in the category (A) will be relieved from tedious combina- torial arguments in several problems. Those in the category (B) will discover the potential of the toric Mori theory. As applications, we treat the Zariski decomposition on toric varieties and the partial resolutions of non-degenerate hypersurface singularities. By these applications, the reader will learn to use the toric Mori theory.
Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/1fc0f937cf41587a4b17180c0e389bfadb1cc314
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In Algebra and Number Theory
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Citations in the corpus
- Canonical Toric Fano Threefolds (2008, background): “FS04 ]). There are eighteen smooth toric Fano threefolds ([Bat81, Bat91, WW82]), and 124 smooth toric Fano fourfolds ([Bat99, Sat00]).”