Open Access
Translator Disclaimer
January 2022 Boundedness of log-pluricanonical maps for surfaces of log-general type in positive characteristic
Omprokash Das
Author Affiliations +
Osaka J. Math. 59(1): 65-74 (January 2022).

Abstract

In this article we prove the following boundedness result: Fix a DCC set $I\subset [0, 1]$. Let $\mathfrak{D}$ be the set of all log pairs $(X, \Delta)$ satisfying the following properties: (i) $X$ is a projective surface defined over an algebraically closed field, (ii) $(X, \Delta)$ is log canonical and the coefficients of $\Delta$ are in $I$, and (iii) $K_X+\Delta$ is big. Then there is a positive integer $N=N(I)$ depending only on the set $I$ such that the linear system $|\lfloor m(K_X+\Delta)\rfloor|$ defines a birational map onto its image for all $m\geq N$ and $(X, \Delta)\in\mathfrak{D}$.

Acknowledgments

The author would like to thank Christopher Hacon for answering his questions.

Citation

Download Citation

Omprokash Das. "Boundedness of log-pluricanonical maps for surfaces of log-general type in positive characteristic." Osaka J. Math. 59 (1) 65 - 74, January 2022.

Information

Received: 17 August 2020; Revised: 29 September 2020; Published: January 2022
First available in Project Euclid: 31 January 2022

Subjects:
Primary: 14E05 , 14E30 , 14J29

Rights: Copyright © 2022 Osaka University and Osaka City University, Departments of Mathematics

JOURNAL ARTICLE
10 PAGES


SHARE
Vol.59 • No. 1 • January 2022
Back to Top