Birational smooth minimal models have equal Hodge numbers in all dimensions. (English) Zbl 1051.14012
Yui, Noriko (ed.) et al., Calabi-Yau varieties and mirror symmetry. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3355-3/hbk). Fields Inst. Commun. 38, 183-194 (2003).
The paper under review proves, by means of reduction modulo \(p\) and \(p\)-adic integration, the equivalence of Hodge numbers for smooth minimal models defined over the complex field. The statement has been obtained by similar methods by C.-L. Wang [J. Differ. Geom. 60, No. 2, 345–354 (2002; Zbl 1052.14016)] and via motivic integration by W. Veys [Can. J. Math. 53, No. 4, 834–865 (2001; Zbl 1073.14501)].
For the entire collection see [Zbl 1022.00014].
For the entire collection see [Zbl 1022.00014].
Reviewer: Massimiliano Mella (Ferrara)
MSC:
| 14E05 | Rational and birational maps |
| 14C30 | Transcendental methods, Hodge theory (algebro-geometric aspects) |
| 11S80 | Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.) |
| 14E30 | Minimal model program (Mori theory, extremal rays) |
