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: strong Lefschetz hyperplane theorem | Statement: [Lefschetz hyperplane theorem, hasVersion, strong Lefschetz hyperplane theorem]

Target entity: strong Lefschetz hyperplane theorem
Context triple: [Lefschetz hyperplane theorem, hasVersion, strong Lefschetz hyperplane theorem]

• A. Lefschetz hyperplane theorem
  The Lefschetz hyperplane theorem is a fundamental result in algebraic geometry and topology that relates the topology (especially homology and homotopy groups) of a smooth projective variety to that of its hyperplane sections.
• B. Hard Lefschetz theorem chosen
  The Hard Lefschetz theorem is a fundamental result in algebraic geometry and Hodge theory that relates the cohomology groups of a compact Kähler manifold via repeated cup product with the Kähler class, yielding powerful symmetry and duality properties.
• C. Grothendieck–Lefschetz theorem
  The Grothendieck–Lefschetz theorem is a fundamental result in algebraic geometry that extends Lefschetz-type hyperplane theorems to a broad scheme-theoretic and cohomological setting, relating the geometry and Picard groups of a variety to those of its hyperplane sections.
• D. Kodaira vanishing theorem
  The Kodaira vanishing theorem is a fundamental result in algebraic geometry that gives conditions under which certain cohomology groups of ample line bundles on smooth projective varieties vanish, with deep implications for the classification of complex manifolds.
• E. Serre vanishing theorem
  The Serre vanishing theorem is a fundamental result in algebraic geometry stating that, on a projective variety, sufficiently high tensor powers of an ample line bundle have vanishing higher cohomology groups.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.