Aspects of enumerative geometry with quadratic forms

Abstract

We develop various aspects of classical enumerative geometry, including Euler characteristics and formulas for counting degenerate fibres in a pencil, with the classical numerical formulas being replaced by identitites in the Grothendieck-Witt group of quadratic forms with coefficients in the base-field.

The paper has appeared in Documenta. This version corrects a few typos

References in corpus (3)

• Fundamental classes in motivic homotopy theory
• On the relation of Voevodsky's algebraic cobordism to Quillen's K-theory
• Chow-Witt rings of Grassmannians

Cited by in corpus (10)

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• Künneth formulas for motives and additivity of traces
• The unit map of the algebraic special linear cobordism spectrum
• Toward an algebraic theory of Welschinger invariants
• An Example of Wild Ramification in an Enriched Riemann-Hurwitz Formula
• Algebraic elliptic cohomology and flops II: $SL$-cobordism
• On the ${\mathbb{A}}^1$-Euler characteristic of the variety of maximal tori in a reductive group
• Conics meeting eight lines over perfect fields