geometry, the minimal model program is part of the birational classification of algebraic varieties. Its goal is to construct a birational model of any complex...

in the minimal model program, given by blowing up along a relative canonical ring. In dimension 3 flips are used to construct minimal models, and any...

problem, which is called the algebrization conjecture via analytical minimal model program. Suppose ( X , g ) {\displaystyle (X,g)} is a Riemannian manifold...

of Mori's results to dimensions higher than three is called the minimal model program and is an active area of research in algebraic geometry. He has...

proof of boundedness of Fano varieties and contributions to the minimal model program". In his office at the University, Birkar has two photographs of...

University. Xu is known for his work in birational geometry, the minimal model program, and the K-stability of Fano varieties. After completing his PhD...

(1980). Terminal singularities are important in the minimal model program because smooth minimal models do not always exist, and thus one must allow certain...

coincides with the minimal Herbrand model of the program. The fixpoint semantics suggest an algorithm for computing the minimal Herbrand model: Start with the...

Project, Tag 0AFW. "Chapter 2. Preliminaries". Foundations of the minimal model program. Mathematical Society of Japan Memoirs. 2017. pp. 16–47. doi:10...

Cohen–Macaulay. Toric varieties over any field are Cohen–Macaulay. The minimal model program makes prominent use of varieties with klt (Kawamata log terminal)...

especially in traditional problems in algebraic geometry. Famously the minimal model program was used to construct moduli spaces of varieties of general type...

1, "Book on Moduli of Surfaces". Mori's minimal model program The minimal model program is a research program aiming to do birational classification of...

of complex manifolds and complex algebraic varieties through the minimal model program and the construction of moduli spaces sets the field apart from...

an ancient Egyptian mathematical papyrus Matrilysin, an enzyme Minimal model program, a branch of birational geometry Million progressive motile (million...

Caraiani – "For diverse transformative contributions to the Langlands program, and in particular for work with Peter Scholze on the Hodge-Tate period...

in higher dimensions is referred to as birational geometry. The minimal model program attempts to identify the simplest (in a certain precise sense) algebraic...

In algebraic geometry, the Néron model (or Néron minimal model, or minimal model) for an abelian variety AK defined over the field of fractions K of a...

The Minimal Supersymmetric Standard Model (MSSM) is an extension to the Standard Model that realizes supersymmetry. MSSM is the minimal supersymmetrical...

map, where k is any sufficiently divisible positive integer. The minimal model program proposed that the canonical ring of every smooth or mildly singular...

definition, one could assume that X is smooth over a field, but the minimal model program has also led to the study of Fano varieties with various types of...

See also Shimura variety. Using techniques arising out of the minimal model program, moduli spaces of varieties of general type were constructed by...

Chomsky. Following Imre Lakatos's distinction, Chomsky presents minimalism as a program, understood as a mode of inquiry that provides a conceptual framework...

positive dimension. The ones arising from extremal contractions in the minimal model program are called Mori fibrations or Mori fiber spaces (for Shigefumi Mori)...

Unirational variety Ruled variety Kodaira dimension Canonical ring Minimal model program Intersection theory Intersection number Chow ring Chern class Serre's...

conjecture is a conjecture in birational geometry, more precisely in the minimal model program, stating that for every projective variety X {\displaystyle X} with...

Princeton University. Kollár is known for his contributions to the minimal model program for threefolds and hence the compactification of moduli of algebraic...

equivalence relation Hilbert scheme Lefschetz hyperplane theorem Minimal model program Kollár & Moduli, Ch I. Shafarevich, Igor R. (1994), Basic Algebraic...

ISBN 978-3-540-03603-6, MR 0222093 Kollár, János (2013), Singularities of the Minimal Model Program, Cambridge University Press, ISBN 978-1-107-03534-8, MR 3057950...

affirmatively the problem of whether they are Cohen–Macaulay. The minimal model program started by Shigefumi Mori proved that the sheaf in the definition...

fundamental to the classification of algebraic varieties and the minimal model program. Kodaira vanishing fails over fields of positive characteristic...