Topological Methods in Algebraic Geometry

E586797

mathematics book monograph nonfiction book

Topological Methods in Algebraic Geometry is a foundational mathematical monograph by Friedrich Hirzebruch that applies topological techniques, particularly characteristic classes and cobordism theory, to problems in algebraic geometry.

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All labels observed (3)

Label	Occurrences
Hirzebruch’s book "Neue topologische Methoden in der algebraischen Geometrie"	1
Topological Methods in Algebraic Geometry canonical	1
Topologische Methoden in der algebraischen Geometrie	1

How this entity was disambiguated

This entity first appeared as the object of triple T6337383 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07

Target entity: Topological Methods in Algebraic Geometry
Context triple: [Friedrich Hirzebruch, notableWork, Topological Methods in Algebraic Geometry]

A. Foundations of Algebraic Geometry
Foundations of Algebraic Geometry is a landmark mathematical treatise that systematically developed the modern foundations of algebraic geometry and profoundly influenced the field’s subsequent evolution.
B. Chevalley’s theorem in algebraic geometry
Chevalley’s theorem in algebraic geometry is a fundamental result stating that the image of a morphism of finite type between schemes (or varieties) is a constructible set, playing a key role in understanding how geometric properties behave under mappings.
C. L’Analysis Situs et la Géométrie Algébrique
L’Analysis Situs et la Géométrie Algébrique is a foundational mathematical treatise that helped establish modern algebraic topology and its connections with algebraic geometry.
D. Singular Points of Complex Hypersurfaces
"Singular Points of Complex Hypersurfaces" is a foundational monograph in singularity theory that systematically studies the local and topological properties of singularities arising in complex algebraic and analytic hypersurfaces.
E. Brill–Noether theory
Brill–Noether theory is a branch of algebraic geometry that studies linear series on algebraic curves, particularly the existence and dimension of spaces of special divisors and maps to projective spaces.
F. None of above. chosen
G. Unsure - the case is ambiguous/there is not enough information to decide.

NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07

Target entity: Topological Methods in Algebraic Geometry
Target entity description: Topological Methods in Algebraic Geometry is a foundational mathematical monograph by Friedrich Hirzebruch that applies topological techniques, particularly characteristic classes and cobordism theory, to problems in algebraic geometry.

A. Foundations of Algebraic Geometry
Foundations of Algebraic Geometry is a landmark mathematical treatise that systematically developed the modern foundations of algebraic geometry and profoundly influenced the field’s subsequent evolution.
B. Chevalley’s theorem in algebraic geometry
Chevalley’s theorem in algebraic geometry is a fundamental result stating that the image of a morphism of finite type between schemes (or varieties) is a constructible set, playing a key role in understanding how geometric properties behave under mappings.
C. L’Analysis Situs et la Géométrie Algébrique
L’Analysis Situs et la Géométrie Algébrique is a foundational mathematical treatise that helped establish modern algebraic topology and its connections with algebraic geometry.
D. Singular Points of Complex Hypersurfaces
"Singular Points of Complex Hypersurfaces" is a foundational monograph in singularity theory that systematically studies the local and topological properties of singularities arising in complex algebraic and analytic hypersurfaces.
E. Brill–Noether theory
Brill–Noether theory is a branch of algebraic geometry that studies linear series on algebraic curves, particularly the existence and dimension of spaces of special divisors and maps to projective spaces.
F. None of above. chosen

Statements (46)

Predicate	Object
instanceOf	mathematics book ⓘ monograph ⓘ nonfiction book ⓘ
academicDiscipline	pure mathematics ⓘ
author	Friedrich Hirzebruch ⓘ
field	algebraic geometry ⓘ differential topology ⓘ topology ⓘ
hasAudience	graduate students in mathematics ⓘ research mathematicians ⓘ
hasContribution	bridging complex geometry and algebraic topology ⓘ development of topological approach to the Riemann–Roch theorem ⓘ introduction of cobordism ideas into algebraic geometry ⓘ systematic use of characteristic classes in algebraic geometry ⓘ
hasSubject	Hirzebruch genus ⓘ linked to: Hirzebruch genera Todd class ⓘ cohomology of complex manifolds ⓘ complex projective varieties ⓘ multiplicative sequences of characteristic classes ⓘ signature theorem ⓘ topological invariants of algebraic varieties ⓘ
influenced	modern algebraic geometry ⓘ modern algebraic topology ⓘ theory of characteristic classes ⓘ
language	German ⓘ
notableFor	classic status in 20th-century geometry literature ⓘ foundational exposition of topological techniques in algebraic geometry ⓘ influence on the development of cobordism theory ⓘ
originalTitle	Topologische Methoden in der algebraischen Geometrie ⓘ linked to: Topological Methods in Algebraic Geometry
publisher	Springer ⓘ
relatedWork	Atiyah–Singer index theorem ⓘ Characteristic Classes by Milnor and Stasheff ⓘ Hirzebruch–Riemann–Roch theorem ⓘ
series	Grundlehren der mathematischen Wissenschaften ⓘ linked to: Die Grundlehren der mathematischen Wissenschaften
timePeriod	20th century ⓘ
topic	Chern classes ⓘ Hirzebruch–Riemann–Roch theorem ⓘ K-theory (topology) ⓘ linked to: K-theory characteristic classes ⓘ cobordism theory ⓘ complex manifolds ⓘ holomorphic vector bundles ⓘ intersection theory ⓘ topological methods in algebraic geometry ⓘ
usedAs	graduate-level textbook ⓘ reference work for researchers in geometry ⓘ

How these facts were elicited

Referenced by (3)

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

Friedrich Hirzebruch → notableWork → Topological Methods in Algebraic Geometry ⓘ

Hirzebruch genera → appearsIn → Hirzebruch’s book "Neue topologische Methoden in der algebraischen Geometrie" ⓘ

linked to: Topological Methods in Algebraic Geometry

Topological Methods in Algebraic Geometry → originalTitle → Topologische Methoden in der algebraischen Geometrie ⓘ