Notes on toric varieties from Mori theoretic viewpoint, II
Osamu Fujino,Hiroshi Sato +1 more
TLDR
In this article, the lengths of extremal rays of Birational type for toric varieties are given. But they do not consider the effects of adjoint bundles of projective toric bundles.Abstract:
We give new estimates of lengths of extremal rays of birational type for toric varieties. We can see that our new estimates are the best by constructing some examples explicitly. As applications, we discuss the nefness and pseudo-effectivity of adjoint bundles of projective toric varieties. We also treat some generalizations of Fujita's freeness and very ampleness for toric varieties.read more
Citations
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Journal ArticleDOI
Introduction to the toric mori theory
Osamu Fujino,Hiroshi Sato +1 more
TL;DR: The main purpose of as discussed by the authors is to give a simple and non-combinatorial proof of the toric Mori theory, which means the log-minimal model program (MMP) for toric varieties.
Posted Content
Weighted projective spaces from the toric point of view with computational applications.
Michele Rossi,Lea Terracini +1 more
TL;DR: In this article, the authors give a sur- vey on weighted projective spaces by the toric point of view, which seems to be missing in the literature, and provide characterizations of fans and poly- topes giving (polarized, in case) weighted projectively spaces, so inaugurating a kind of recognition process of toric data like fans.
Dissertation
Toric Fano varieties and convex polytopes
TL;DR: In this article, the authors study toric Fano varieties, which are convex lattice polytopes whose boundary lattice points are dictated by the singularities involved in the polytope.
Journal ArticleDOI
Linear determinantal equations for all projective schemes
Jessica Sidman,Gregory G. Smith +1 more
TL;DR: In this paper, it was shown that every projective embedding of a connected scheme determined by the complete linear series of a sufficiently ample line bundle is defined by the 2 � 2 minors of a 1-generic matrix of linear forms.
References
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Book
Birational Geometry of Algebraic Varieties
János Kollár,Shigefumi Mori +1 more
TL;DR: In this paper, the authors introduce the minimal model program and the canonical class of rational curves, and present the singularities of the model program, as well as three dimensional flops.
Proceedings ArticleDOI
Introduction to the Minimal Model Problem
Journal ArticleDOI
Characterizations of complex projective spaces and hyperquadrics
TL;DR: In this article, the Ricci curvature of a Kdhler manifold has been characterized in terms of the first Chern class of a manifold, which is closely related to Ricci's curvature.