Introduction to the Mori Program

By 松木 謙二. 2002

273 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/9d02a933839380b8f693a05488209e7a8909663a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

1. M. Mustaţă
2. Y. Ruan
3. L. Ein
4. C. Birkar
5. Paul Blain Levy
6. O. Fujino
7. E. Sommers
8. Karl Schwede

Citations in the corpus

• Arc spaces, motivic integration and stringy invariants (2004, unknown): “in [KM][KMM][Ma].”
• Log homogeneous varieties (2006, background): “Our arguments are purely algebraic; they involve results of the theory of algebraic transformation groups, and some basic notions borrowed from logarithmic birational geometry (for which we refer to [15]) and holomorphic transformation groups (see [1, 10]).”
• Generic singularities of nilpotent orbit closures (2015, background): “A general reference for minimal model program in algebraic geometry is [Mat02].”
• The F-theory geometry with most flux vacua (2015, methodology): “While this story involves Mori theory [54] and is much more complicated in various ways, at a rough level we expect the minimal threefolds supporting elliptic Calabi-Yau fourfolds to be one of three types: Fano threefolds, P1 bundles (or more general conic bundles) over complex surfaces B, and bundl”
• Introduction to the log minimal model program for log canonical pairs (2009, background): “It is not a good idea to read this book without studying the classical results discussed in [KM], [KMM], or [M].”
• Bounds for log canonical thresholds with applications to birational rigidity (2002, background): “By the Noether-Fano inequality (see [Co1] and [Isk], or [Mat]), we find a linear subsystem H ⊂ |OX(r)|, with r ≥ 1, whose base scheme B has codimension ≥ 2, and such that the pair (X, 1r · B) is not canonical.”
• Twisted cubics on cubic fourfolds (2013, background): “es [] generate a ray. Moreover, as O D(D) is negative on the fibres of ˇby (4.19) and K Z0˘mD, the restriction of K Z0to this ray is strictly negative. Using the Contraction Theorem ([25] Thm. 3.7, or [24] Thm. 8-3-1) we conclude: There is a morphism Z0!Zwith the following properties: (1) Zis normal ”
• Log Crepant Birational Maps and Derived Categories (2003, background): “By [8] with some additional argument due to Matsuki, f is shown to be decomposed into a sequence of divisorial contractions and flips which are log crepant.”