Noether’s formula

E898499

result in complex geometry theorem in algebraic geometry

Noether’s formula is a fundamental result in algebraic geometry that relates the holomorphic Euler characteristic of a smooth projective surface to its Chern numbers, serving as a special case of the Hirzebruch–Riemann–Roch theorem.

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All labels observed (1)

Label	Occurrences
Noether’s formula canonical	1

Statements (44)

Predicate	Object
instanceOf	result in complex geometry ⓘ theorem in algebraic geometry ⓘ
appearsIn	birational geometry of surfaces ⓘ theory of minimal models of surfaces ⓘ
appliesTo	complex algebraic surface ⓘ smooth projective surface ⓘ
assumes	surface is defined over the complex numbers ⓘ surface is projective ⓘ surface is smooth ⓘ
connectedTo	Chern–Gauss–Bonnet theorem NERFINISHED ⓘ Enriques–Kodaira classification NERFINISHED ⓘ Noether’s inequality NERFINISHED ⓘ Todd class NERFINISHED ⓘ
expresses	holomorphic Euler characteristic in terms of Chern numbers ⓘ
field	algebraic geometry ⓘ complex geometry ⓘ topology of complex surfaces ⓘ
hasConsequence	constraints on possible Chern numbers of surfaces ⓘ relations between arithmetic genus and Chern classes ⓘ
hasDomain	compact complex surfaces ⓘ
hasRole	bridge between analytic and algebraic invariants of surfaces ⓘ
historicalPeriod	early 20th century mathematics ⓘ
involves	canonical divisor ⓘ first Chern class ⓘ holomorphic Euler characteristic of the structure sheaf ⓘ second Chern class ⓘ structure sheaf ⓘ
isSpecialCaseOf	Hirzebruch–Riemann–Roch theorem NERFINISHED ⓘ
mathematicalArea	birational classification of surfaces ⓘ intersection theory ⓘ sheaf cohomology ⓘ
namedAfter	Emmy Noether NERFINISHED ⓘ
relatedConcept	Chern numbers c1^2 and c2 ⓘ arithmetic genus ⓘ geometric genus ⓘ holomorphic Euler characteristic ⓘ irregularity of a surface ⓘ
relates	Chern numbers NERFINISHED ⓘ holomorphic Euler characteristic ⓘ topological invariants of surfaces ⓘ
typeOf	Riemann–Roch type formula NERFINISHED ⓘ
usedFor	classification of algebraic surfaces ⓘ computing invariants of surfaces ⓘ relating geometric and topological data of surfaces ⓘ

Referenced by (1)

Full triples — surface form annotated when it differs from this entity's canonical label.

Hirzebruch–Riemann–Roch theorem → relatedTo → Noether’s formula ⓘ