The Enumerative Theory of Conics after Halphen

Inhaltsverzeichnis

• Conics.
• Complete conics.
• Systems of conics.
• Equations of the degeneration hypersurfaces.
• Conditions imposed on conics.
• Action of the projective group and proper solutions of an enumarative problem.
• Genericity of the data of conditions.
• Local characters of a condition.
• Halphen's first formula.
• Computation of characteristic numbers.
• Examples.
• Strict equivalence of conditions.
• Systems of conics contained in Sp, q.
• Conics satisfying five independent conditions.
• Cycles on W and on B.
• Multiplicity cycles and Noether's formula.
• Improper intersection numbers.
• Generalization of Halphen's formula to conditions of higher order.
• Examples of higher order conditions.
• Enumerative ring of W.
• Computation of products in hal· (W).
• Further examples.