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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].

##### 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)
##### Keywords:
minimal model; $$p$$-adic Hodge theory; Hodge numbers
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