|
|||||
 |
|
|
|
|
|
|
|
Positivity functions
for curves on algebraic varieties
Brian Lehmann and Jian Xiao |
|
Vol. 13 (2019), No. 6, 1243–1279
|
|
DOI: 10.2140/ant.2019.13.1243
|
Abstract |
|
This is the second part of our work on Zariski decomposition structures, where we compare two different volume type functions for curve classes. The first function is the polar transform of the volume for divisor classes. The second function captures the asymptotic geometry of curves analogously to the volume function for divisors. We prove that the two functions coincide, generalizing Zariski’s classical result for surfaces to all varieties. Our result confirms the log concavity conjecture of the first named author for weighted mobility of curve classes in an unexpected way, via Legendre–Fenchel type transforms. During the course of the proof, we obtain a refined structure theorem for the movable cone of curves. |
PDF Access Denied
We have not been able to recognize your IP address
52.15.63.145
as that of a subscriber to this journal.
Online access to the content of recent issues is by
subscription, or purchase of single articles.
Please contact your institution's librarian suggesting a subscription, for example by using our journal-recommendation form. Or, visit our subscription page for instructions on purchasing a subscription.
You may also contact us at
contact@msp.org
or by using our
contact form.
Or, you may purchase this single article for USD 40.00:
Keywords
algebraic varieties, positivity of curves, mobility of
cycles, volume-type function, Zariski decomposition
|
Mathematical Subject Classification 2010
Primary: 14C25
Secondary: 14C20, 32J25
|
Milestones
Received: 2 March 2018
Revised: 20 February 2019
Accepted: 8 April 2019
Published: 18 August 2019
|
Authors |
| Brian Lehmann | |
| Department of Mathematics Boston College Chestnut Hill, MA United States |
|
| Jian Xiao | |
| Department of Mathematical Sciences
and Yau Mathematical Sciences Center Tsinghua University Beijing China |
|
