Английская Википедия:Behrend function

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In algebraic geometry, the Behrend function of a scheme X, introduced by Kai Behrend, is a constructible function

<math>\nu_X: X \to \mathbb{Z}</math>

such that if X is a quasi-projective proper moduli scheme carrying a symmetric obstruction theory, then the weighted Euler characteristic

<math>\chi(X, \nu_X) = \sum_{n \in \mathbb{Z}} n \, \chi(\{\nu_X = n\})</math>

is the degree of the virtual fundamental class

<math>[X]^{\text{vir}}</math>

of X, which is an element of the zeroth Chow group of X. Modulo some solvable technical difficulties (e.g., what is the Chow group of a stack?), the definition extends to moduli stacks such as the moduli stack of stable sheaves (the Donaldson–Thomas theory) or that of stable maps (the Gromov–Witten theory).

References

• Шаблон:Citation.

Шаблон:Algebraic-geometry-stub