Okounkov Bodies and Restricted Volumes along Very General Curves
نویسنده
چکیده
Given a big divisor D on a normal complex projective variety X , we show that the restricted volume of D along a very general complete-intersection curve C ⊂ X can be read off from the Okounkov body of D with respect to an admissible flag containing C. From this we deduce that if two big divisors D1 and D2 on X have the same Okounkov body with respect to every admissible flag, then D1 and D2 are numerically equivalent.
منابع مشابه
On volumes of arithmetic line bundles
We show an arithmetic generalization of the recent work of Lazarsfeld–Mustaţǎ which uses Okounkov bodies to study linear series of line bundles. As applications, we derive a log-concavity inequality on volumes of arithmetic line bundles and an arithmetic Fujita approximation theorem for big line bundles.
متن کاملOn Volumes of Arithmetic Line Bundles II
This paper uses convex bodies to study line bundles in the setting of Arakelov theory. The treatment is parallel to [Yu2], but the content is independent. The method of constructing a convex body in Euclidean space, now called “Okounkov body”, from a given algebraic linear series was due to Okounkov [Ok1, Ok2], and was explored systematically by Kaveh–Khovanskii [KK] and Lazarsfeld–Mustaţǎ [LM]...
متن کاملNewton-okounkov Convex Bodies of Schubert Varieties and Polyhedral Realizations of Crystal Bases
A Newton-Okounkov convex body is a convex body constructed from a projective variety with a valuation on its homogeneous coordinate ring; this is deeply connected with representation theory. For instance, the Littelmann string polytopes and the Feigin-Fourier-Littelmann-Vinberg polytopes are examples of Newton-Okounkov convex bodies. In this paper, we prove that the NewtonOkounkov convex body o...
متن کاملVolume difference inequalities for the projection and intersection bodies
In this paper, we introduce a new concept of volumes difference function of the projection and intersection bodies. Following this, we establish the Minkowski and Brunn-Minkowski inequalities for volumes difference function of the projection and intersection bodies.
متن کاملA Simple Proof of Mirzakhani’s Recursion Formula of Weil-petersson Volumes
In this paper, we give a simple proof of Mirzakhani's recursion formula of Weil-Petersson volumes of moduli spaces of curves using the Witten-Kontsevich theorem. We also briefly describe a very general recursive phenomenon in the intersection theory of moduli spaces of curves. In particular, we present several new recursion formulas for higher degree κ classes.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009