TY - JOUR
T1 - Newton–Okounkov bodies sprouting on the valuative tree
AU - Ciliberto, Ciro
AU - Farnik, Michal
AU - Küronya, Alex
AU - Lozovanu, Victor
AU - Roé, Joaquim
AU - Shramov, Constantin
PY - 2017/8/1
Y1 - 2017/8/1
N2 - © 2016, Springer-Verlag Italia. 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.
AB - © 2016, Springer-Verlag Italia. 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.
KW - Algebraic geometry
KW - Linear system
KW - Newton-Okounkov body
KW - Valuation
KW - Valuative tree
U2 - 10.1007/s12215-016-0285-3
DO - 10.1007/s12215-016-0285-3
M3 - Article
SN - 0009-725X
VL - 66
SP - 161
EP - 194
JO - Rendiconti del Circolo Matematico di Palermo
JF - Rendiconti del Circolo Matematico di Palermo
ER -