Abstract
We show that the Nakai–Moishezon ampleness criterion holds for real line bundles on complete schemes. As applications, we treat the relative Nakai–Moishezon ampleness criterion for real line bundles and the Nakai–Moishezon ampleness criterion for real line bundles on complete algebraic spaces. The main ingredient of this paper is Birkar’s characterization of augmented base loci of real divisors on projective schemes.
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Acknowledgements
The first author was partially supported by JSPS KAKENHI Grant numbers JP16H03925, JP16H06337. The second author was partially supported by JSPS KAKENHI Grant number 20J20070. The authors thank Yoshinori Gongyo and Kenta Hashizume for comments. They also thank Professor János Kollár for informing them that he obtained an alternative proof of Theorem 1.3 without using Birkar’s theorem.
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Communicated by Vasudevan Srinivas.
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Fujino, O., Miyamoto, K. Nakai–Moishezon ampleness criterion for real line bundles. Math. Ann. 385, 459–470 (2023). https://doi.org/10.1007/s00208-021-02354-9
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DOI: https://doi.org/10.1007/s00208-021-02354-9