Newton-Okounkov bodies sprouting on the valuative tree
Ciliberto, Ciro (Università di Roma. Dipartimento di Matematica)
Farnik, Michal (Jagiellonian University (Polònia). Faculty of Mathematics and Computer Science)
Küronya, Alex (Goethe-Universität Frankfurt am Main. Institut für Mathematik)
Lozovanu, Victor (Université de Caen Normandie. Laboratoire de Mathématiques)
Roé Vellvé, Joaquim (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Shramov, Constantin

Data:	2016
Resum:	Given a smooth projective algebraic surface X, a point O∈X and a big divisor D on X, we consider the set of all Newton-Okounkov bodies of D with respect to valuations of the field of rational functions of X centred at O, or, equivalently, with respect to a flag (E, p) which is infinitely nearO, in the sense that there is a sequence of blowups X'→X, mapping the smooth, irreducible rational curve E⊂X' to O. The main objective of this paper is to start a systematic study of the variation of these infinitesimal Newton-Okounkov bodies as (E, p) varies, focusing on the case X=P2.
Ajuts:	Ministerio de Economía y Competitividad MTM2013-40680-P
Nota:	Agraïments: This research was started during the workshop "Recent advances in Linear series and Newton-Okounkov bodies", which took place in Padova, Italy, February 9-14, 2015. The authors enjoyed the lively and stimulating atmosphere of that event. Michal Farnik was partially supported by the Polish National Science Centre, grant number 2015/17/B/ST1/02637. Constantin Shramov was partially supported by the Russian Academic Excellence Project 5-100', by RFBR grants 15-01-02164, 15-01-02158, 14-01-00160, and by Dynasty foundation.
Drets:	Tots els drets reservats.
Llengua:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Matèria:	Newton-Okounkov body ; Valuative tree ; Valuation ; Linear system ; Algebraic geometry
Publicat a:	Rendiconti del Circolo Matematico di Palermo, 2016 , ISSN 1973-4409

DOI: 10.1007/s12215-016-0285-3

Post-print 34 p, 480.3 KB

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