Triple

Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).

Phrase: Schubert varieties | Statement: [Kazhdan–Lusztig theory, mainObjectOfStudy, Schubert varieties]

Target entity: Schubert varieties
Context triple: [Kazhdan–Lusztig theory, mainObjectOfStudy, Schubert varieties]

• A. 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.
• B. Lazarsfeld’s Positivity in Algebraic Geometry
  Lazarsfeld’s *Positivity in Algebraic Geometry* is a two-volume monograph that serves as a standard modern reference on the theory of positivity for line bundles and divisors in algebraic geometry, integrating techniques from cohomology, vanishing theorems, and birational geometry.
• C. Topological Methods in Algebraic Geometry
  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.
• D. Clebsch–Aronhold invariants
  The Clebsch–Aronhold invariants are classical algebraic invariants associated with binary forms, particularly quartic forms, that play a key role in invariant theory and the classification of algebraic curves.
• E. Serre’s theorem on projective embeddings via ample line bundles
  Serre’s theorem on projective embeddings via ample line bundles is a foundational result in algebraic geometry that characterizes when a variety can be embedded into projective space using sufficiently high tensor powers of an ample line bundle.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Schubert varieties
Target entity description: Schubert varieties are special subvarieties of flag varieties that play a central role in algebraic geometry and representation theory, particularly in the study of singularities and intersection cohomology.

• A. 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.
• B. Lazarsfeld’s Positivity in Algebraic Geometry
  Lazarsfeld’s *Positivity in Algebraic Geometry* is a two-volume monograph that serves as a standard modern reference on the theory of positivity for line bundles and divisors in algebraic geometry, integrating techniques from cohomology, vanishing theorems, and birational geometry.
• C. Topological Methods in Algebraic Geometry
  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.
• D. Clebsch–Aronhold invariants
  The Clebsch–Aronhold invariants are classical algebraic invariants associated with binary forms, particularly quartic forms, that play a key role in invariant theory and the classification of algebraic curves.
• E. Serre’s theorem on projective embeddings via ample line bundles
  Serre’s theorem on projective embeddings via ample line bundles is a foundational result in algebraic geometry that characterizes when a variety can be embedded into projective space using sufficiently high tensor powers of an ample line bundle.
• F. None of above. chosen