A review of geometrically defined functions on Newton–Okounkov bodies

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Abstract

This note is a presentation of two functions carrying geometric information recently defined on the Newton–Okounkov body by Boucksom and Chen (Compos Math 147:1205–1229, 2011) and Nystrom (Ann Sci ÉC Norm Supér (4) 47:1111–1161, 2014). None of the material presented here is original, and much can also be found in Boucksom’s (Séminaire Bourbaki, 2012) Bourbaki talk.

Keywords

Newton–Okounkov bodies Valuations 

Mathematics Subject Classification

14E99 
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Notes

Acknowledgements

The author wishes to thank the anonymous referee, whose careful reading has much improved the presentation of this note.

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Copyright information

© Springer-Verlag Italia 2017

Authors and Affiliations

  1. 1.Institut FourierUniversité Grenoble AlpesGrenobleFrance

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