Boundedness of Log Canonical Surface Generalized Polarized Pairs

Autor:	Stefano Filipazzi
Rok vydání:	2018
Předmět:	Surface (mathematics) volume 14J10 General Mathematics boundedness generalized polarized pair 14E30 Combinatorics Mathematics - Algebraic Geometry Mathematics::Algebraic Geometry Bounded function FOS: Mathematics 14J29 Algebraic Geometry (math.AG) DCC Mathematics
Zdroj:	Taiwanese J. Math. 22, no. 4 (2018), 813-850
ISSN:	1027-5487
DOI:	10.11650/tjm/171204
Popis:	In this paper, we study the behavior of the sets of volumes of the form $\mathrm{vol}(X,K_X+B+M)$, where $(X,B)$ is a log canonical pair, and $M$ is a nef $\mathbb{R}$-divisor. After a first analysis of some general properties, we focus on the case when $M$ is $\mathbb{Q}$-Cartier with given Cartier index, and $B$ has coefficients in a given DCC set. First, we show that such sets of volumes satisfy the DCC property in the case of surfaces. Once this is established, we show that surface pairs with given volume and for which $K_X+B+M$ is ample form a log bounded family. These generalize results due to Alexeev [Ale94]. 32 pages, comments are welcome
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::291c6221001c45cf8c6437d677d6df35 https://doi.org/10.11650/tjm/171204 Zobrazit plný text záznamu