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- W2316971531 abstract "Introduction. In this paper we study the Chow variety of a maximal, total, regular family of positive divisors on a non-singular projective variety V. An algebraic family t of positive divisors on v is called maximal if 't is not a proper subset of another algebraic family; it is called total if for every divisor Y on V, algebraically equivalent to zero, and for an arbitrary fixed (i. e. independent of Y) XO C 'it there exists an X C 'i such that Y, X X,0 (means linear equivalence) ; finally, it is called regular if for every pair X, X' C 't we have I (X) = I (X'), where I (X) denotes the dimension of the linear system determined by X. These definitions are introduced, and the existence of such families is proved, in [6, 7] (in [6, 7] such families are called maximal, regular, complete instead of maximal, total, regular in this order). If V is embedded in projective space pN, then the Chow points are constructed by means of the hyperplanes in pN, and therefore we must expect that there is some connection between the properties of the Chow variety U of ' (for instance the non-singularity of U) and the way V is embedded in pN (or to be more precise, the properties of the linear system of hyperplane sections on V). Our main purpose is to show that, under a mild condition on the embedding of V in pN, the Chow variety of a maximal, total, regular family is non-singular. As a preparation to this result we first study the Chow varieties of linear systems on V and it turns out that, under the same condition on the embedding of v in pN, the Chow variety of a linear system is non-singular (Proposition 1)." @default.
- W2316971531 created "2016-06-24" @default.
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- W2316971531 date "1961-01-01" @default.
- W2316971531 modified "2023-09-26" @default.
- W2316971531 title "On Chow Varieties of Maximal, Total, Regular Families of Positive Divisors" @default.
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- W2316971531 doi "https://doi.org/10.2307/2372723" @default.
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