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Birational geometry

In mathematics, birational geometry is a field of algebraic geometry in which the goal is to determine when two algebraic varieties are isomorphic outside lower-dimensional subsets. This amounts to studying mappings that are given by rational functions rather than polynomials; the map may fail to be defined where the rational functions have poles.

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Overview

Birational maps

Minimal models and resolution of singularities

Birational invariants

Minimal models in higher dimensions

Uniruled varieties

Birational automorphism groups

Applications

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Map overview Semantic statistics

Birational geometry

Nodes64
Edges63
Triples7
Avg. degree1.97
Density0.03125
Components1

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Birational geometry

Top relations

has application · 5
Birational geometry → Birational, Famously, János Kollár, KSB, Nicholas Shepherd-Barron
is a · 1
Birational geometry → field of algebraic geometry in which the goal is to determine when two algebraic varieties are isomorphic outside lower-dimensional subsets

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Important terminology

birational varieties rational smooth projective variety dimension minimal displaystyle algebraic map space mathbb every fano field group two invariants isomorphic

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Birational geometryis afield of algebraic geometry in which the goal is to determine when two algebraic varieties are isomorphic outside lower-dimensional subsets0.90text
Birkar's proof of boundedness of Fano varieties have been used to prove existence results for moduli spacesinstance ofImportant results in birational geometry0.80text
Birational geometryhas applicationBirational0.60section
Birational geometryhas applicationFamously0.60section
Birational geometryhas applicationJános Kollár0.60section
Birational geometryhas applicationNicholas Shepherd-Barron0.60section
Birational geometryhas applicationKSB0.60section

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    Min side: 3
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