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Zbl 0845.14005
Elizondo, Javier
The Euler series of restricted Chow varieties. (English)
[J] Compos. Math. 94, No.3, 297-310 (1994). ISSN 0010-437X; ISSN 1570-5846/e

{\it H. B. Lawson} jun. and {\it S. S.-T. Yau} [Ann. Sci. Éc. Norm. Supér., IV. Sér. 20, 557-577 (1987; Zbl 0639.32015)] introduced a series associated to the Chow monoid of a projective variety that becomes a formal power series when a basis for homology is fixed and they proved it is a rational function for the cases $\bbfP^n$ and $\bbfP^n \times \bbfP^m$. In this paper the author considers the ``restricted'' Chow variety $C_\lambda (X)$ of a projective algebraic variety $X$, i.e. the space consisting of all effective cycles with a given homology class $\lambda$, and he calculates the Euler characteristic of $C_\lambda (X)$ (by introducing a more general Euler series) when $X$ admits a linear action of an algebraic torus, for which there are only finitely many irreducible invariant subvarieties. Then smooth toric varieties are considered and some examples are given.
[Vasile Brinzănescu (MR 96g:14003)]

MSC 2000:: *14C25 Algebraic cycles
14C05 Parametrization
14F45 Topological properties of algebraic varieties

Keywords: restricted Chow variety; Chow monoid; Euler characteristic; Euler series; toric varieties

Citations: Zbl 0639.32015

Cited in: Zbl 0967.14004

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