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.
Ciliberto, C., Farnik, M., Kuronya, A., Lozovanu, V., Shramov, J. (2017). Newton–Okounkov bodies sprouting on the valuative tree. RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO, 66(2), 161-194 [10.1007/s12215-016-0285-3].
Newton–Okounkov bodies sprouting on the valuative tree
C. Ciliberto
;
2017-01-01
Abstract
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.| File | Dimensione | Formato | |
|---|---|---|---|
|
225-Nobodies.pdf
solo utenti autorizzati
Licenza:
Non specificato
Dimensione
1.19 MB
Formato
Adobe PDF
|
1.19 MB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
