Infinitesimal Newton-Okounkov bodies and jet separation

In this paper we explore the connection between asymptotic base loci and Newton-Okounkov bodies associated to infinitesimal flags. Analogously to the surface case, we obtain complete characterizations of augmented and restricted base loci. Interestingly enough, an integral part of the argument is a study of the relationship between certain simplices contained in Newton-Okoukov bodies and jet separation; our results also lead to a convex geometric description of moving Seshadri constants.

[1]  Jinhyung Park,et al.  Asymptotic base loci via Okounkov bodies , 2015, 1507.00817.

[2]  Victor Lozovanu,et al.  Positivity of Line Bundles and Newton-Okounkov Bodies , 2015, Documenta Mathematica.

[3]  A. Sciarretta.  A discrete spacetime model for quantum mechanics , 2015, 1506.00817.

[4]  J. Ro'e.  Local positivity in terms of Newton–Okounkov bodies , 2015, 1505.02051.

[5]  J. Koll'ar,et al.  Volume and Hilbert function of R-divisors , 2015, 1503.02324.

[6]  Victor Lozovanu,et al.  Local positivity of linear series on surfaces , 2014, 1411.6205.

[7]  T. Szemberg.  Minkowski decomposition of Okounkov bodies on surfaces , 2014 .

[8]  S. Boucksom,et al.  Augmented base loci and restricted volumes on normal varieties , 2013, Mathematical Proceedings of the Cambridge Philosophical Society.

[9]  David Anderson,et al.  Okounkov bodies of finitely generated divisors , 2012, 1206.2499.

[10]  C. Maclean,et al.  Convex bodies appearing as Okounkov bodies of divisors , 2010, 1008.4431.

[11]  Kiumars Kaveh,et al.  Newton-Okounkov bodies, semigroups of integral points, graded algebras and intersection theory , 2009, 0904.3350.

[12]  Shin-Yao Jow.  Okounkov bodies and restricted volumes along very general curves , 2009, 0902.2521.

[13]  Robert Lazarsfeld,et al.  Convex Bodies Associated to Linear Series , 2008, 0805.4559.

[14]  M. Nakamaye,et al.  Restricted volumes and base loci of linear series , 2006, math/0607221.

[15]  Luc Capdevila,et al.  Document , 2003 .

[16]  M. Nakamaye.  Base loci of linear series are numerically determined , 2002, math/0204284.

[17]  Andrei Okounkov,et al.  Brunn–Minkowski inequality for multiplicities , 1996 .

[18]  V. Arnold.  Newton-Okounkov bodies, semigroups of integral points, graded algebras and intersection theory , 2012 .

[19]  Robert Lazarsfeld,et al.  Positivity in algebraic geometry , 2004 .