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Theorem of Bertini

In algebraic geometry, the theorem of Bertini is an existence and genericity theorem for smooth connected hyperplane sections for smooth projective varieties over algebraically closed fields, introduced by Eugenio Bertini. This is the simplest and broadest of the "Bertini theorems" applying to a linear system of divisors; simplest because there is no…

Standards, Generalizations & Statement for hyperplane sections of smooth varieties

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Statement for hyperplane sections of smooth varieties

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Generalizations

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Theorem of Bertini

Nodes29
Edges28
Triples18
Avg. degree1.93
Density0.068966
Components1

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Theorem of Bertini

Top relations

related to Generalizations · 11
Theorem of Bertini → Bertini, Borel, For, G-variety, If, Kleiman's, SLn, Steven Kleiman, The, Then, Yσ
related to Statement for hyperplane sections of smooth varieties · 5
Theorem of Bertini → Bertini, If, Let, Recall, The
is a · 2
Theorem of Bertini → existence and genericity theorem for smooth connected hyperplane sections for smooth projective varieties over algebraically closed fields, special case where X

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Important terminology

smooth displaystyle theorem bertini hyperplane system open field sections mathbf subset linear characteristic space projective divisors general varieties hyperplanes dense

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Theorem of Bertiniis aexistence and genericity theorem for smooth connected hyperplane sections for smooth projective varieties over algebraically closed fields0.90text
Theorem of Bertiniis aspecial case where X0.90text
Theorem of Bertinirelated to GeneralizationsThe0.60section
Theorem of Bertinirelated to GeneralizationsBertini0.60section
Theorem of Bertinirelated to GeneralizationsFor0.60section
Theorem of Bertinirelated to GeneralizationsSteven Kleiman0.60section
Theorem of Bertinirelated to GeneralizationsKleiman's0.60section
Theorem of Bertinirelated to GeneralizationsG-variety0.60section
Theorem of Bertinirelated to GeneralizationsYσ0.60section
Theorem of Bertinirelated to GeneralizationsThen0.60section
Theorem of Bertinirelated to GeneralizationsIf0.60section
Theorem of Bertinirelated to GeneralizationsSLn0.60section

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