Cremona group of the projective plane

Target entity: Cremona group of the projective plane
Context triple: [Noether’s AF+BG theorem, relatedTo, Cremona group of the projective plane]

• A. 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.
• B. Veblen axioms for projective geometry
  The Veblen axioms for projective geometry are a foundational set of incidence-based axioms introduced by Oswald Veblen to rigorously formalize the structure of projective spaces.
• C. Clebsch diagonal surfaces
  Clebsch diagonal surfaces are classical 19th-century algebraic surfaces in projective three-space, famous as the first explicit smooth cubic surface with all 27 lines defined over the real numbers.
• D. Erlangen Program
  The Erlangen Program is Felix Klein’s influential 1872 framework that classifies and studies geometries based on their underlying symmetry groups and transformation properties.
• E. The Real Projective Plane
  The Real Projective Plane is a classic mathematical monograph by H. S. M. Coxeter that systematically develops the geometry and topology of the real projective plane, emphasizing its axiomatic foundations and non-Euclidean properties.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Cremona group of the projective plane
Target entity description: The Cremona group of the projective plane is the group of all birational self-maps of the complex projective plane, serving as a fundamental object in algebraic geometry and the study of plane transformations.

• A. 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.
• B. Veblen axioms for projective geometry
  The Veblen axioms for projective geometry are a foundational set of incidence-based axioms introduced by Oswald Veblen to rigorously formalize the structure of projective spaces.
• C. Clebsch diagonal surfaces
  Clebsch diagonal surfaces are classical 19th-century algebraic surfaces in projective three-space, famous as the first explicit smooth cubic surface with all 27 lines defined over the real numbers.
• D. Erlangen Program
  The Erlangen Program is Felix Klein’s influential 1872 framework that classifies and studies geometries based on their underlying symmetry groups and transformation properties.
• E. The Real Projective Plane
  The Real Projective Plane is a classic mathematical monograph by H. S. M. Coxeter that systematically develops the geometry and topology of the real projective plane, emphasizing its axiomatic foundations and non-Euclidean properties.
• F. None of above. chosen