Augmented base loci and restricted volumes on normal varieties, II: The case of real divisors

作者：Lopez Angelo Felice^*

来源：Mathematical Proceedings of the Cambridge Philosophical Society, 2015, 159(3): 517-527.

DOI：10.1017/S030500411500050X

Let X be a normal projective variety defined over an algebraically closed field and let Z be a subvariety. Let D be an R-Cartier R-divisor on X. Given an expression (*) D R-similar to t(1)H(1) + ... + t(s)H(s) with t(i) is an element of R and H-i very ample, we define the (*)-restricted volume of D to Z and we show that it coincides with the usual restricted volume when Z not subset of B+(D). Then, using some recent results of Birkar [Bir], we generalise to R-divisors the two main results of [BCL]: The first, proved for smooth complex projective varieties by Ein, Lazarsfeld, Mustata, Nakamaye and Popa, is the characterisation of B+(D) as the union of subvarieties on which the (*)-restricted volume vanishes; the second is that X - B+(D) is the largest open subset on which the Kodaira map defined by large and divisible (*)-multiples of D is an isomorphism.

• 出版日期2015-11