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AN EXAMPLE CONCERNING ALEXEEVS BOUNDEDNESS RESULTS ON LOG SURFACES
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UNSPECIFIED (1995) AN EXAMPLE CONCERNING ALEXEEVS BOUNDEDNESS RESULTS ON LOG SURFACES. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 118 (Part 1). pp. 6569.
Research output not available from this repository, contact author.Abstract
In this note, we construct a sequence of l.t. surfaces (X(n))(n epsilon N) such that KXn is ample for all n and such that (KXn(2))(n epsilon) is a strictly increasing series with limit equal to 1. This answers (in the affirmative) a question by Alexeev, cf. [A1], 11 . 1. Here, an l.t. surface is a normal complex projective surface with at most quotient singularities (which is the same as 'at most log terminal singularities'). A main result of [Al] implies that it is impossible to find a sequence (X,),,, of l.t. surfaces with K,n ample for all n such that KXn(2) is Strictly decreasing. Although our construction is not too difficult, the example is new and has several interesting implications, see Section 4. Without further explanation, we use some fundamental tools concerning l.t. surfaces like Mumford's intersection theory or the notion of minimality; the reader should consult [Blb] and the references quoted there.
Item Type:  Journal Article  

Subjects:  Q Science > QA Mathematics  
Journal or Publication Title:  MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY  
Publisher:  CAMBRIDGE UNIV PRESS  
ISSN:  03050041  
Official Date:  July 1995  
Dates: 


Volume:  118  
Number:  Part 1  
Number of Pages:  5  
Page Range:  pp. 6569  
Publication Status:  Published 
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