scholarly journals On finiteness of log canonical models

2022 ◽  
Author(s):  
Zhan Li
Keyword(s):  
Convex Set ◽  
Canonical Model ◽  
Canonical Models ◽  
Log Canonical ◽  
Rational Polytope

Let [Formula: see text] be klt pairs with [Formula: see text] a convex set of divisors. Assuming that the relative Kodaira dimensions of such pairs are non-negative, then there are only finitely many log canonical models when the boundary divisors vary in a rational polytope in [Formula: see text]. As a consequence, we show the existence of the log canonical model for a klt pair [Formula: see text] with real coefficients.

scholarly journals A Note on the Issue of Cohesiveness in Canonical Models

2019 ◽  
Vol 29 (3) ◽  
pp. 331-348
Author(s):  
Matteo Pascucci
Keyword(s):  
Modal Logic ◽  
Decision Procedure ◽  
Canonical Model ◽  
Canonical Models

Abstract In their presentation of canonical models for normal systems of modal logic, Hughes and Cresswell observe that some of these models are based on a frame which can be also thought of as a collection of two or more isolated frames; they call such frames ‘non-cohesive’. The problem of checking whether the canonical model of a given system is cohesive is still rather unexplored and no general decision procedure is available. The main contribution of this article consists in introducing a method which is sufficient to show that canonical models of some relevant classes of normal monomodal and bimodal systems are always non-cohesive.

scholarly journals Curves with canonical models on scrolls

2016 ◽  
Vol 27 (05) ◽  
pp. 1650045 ◽  
Author(s):  
Danielle Lara ◽  
Simone Marchesi ◽  
Renato Vidal Martins
Keyword(s):  
Singular Point ◽  
Complete Intersection ◽  
Canonical Model ◽  
Projective Curve ◽  
Canonical Models ◽  
Dimension Formula ◽  
Rational Normal Scroll ◽  
Monomial Curve

Let [Formula: see text] be an integral and projective curve whose canonical model [Formula: see text] lies on a rational normal scroll [Formula: see text] of dimension [Formula: see text]. We mainly study some properties on [Formula: see text], such as gonality and the kind of singularities, in the case where [Formula: see text] and [Formula: see text] is non-Gorenstein, and in the case where [Formula: see text], the scroll [Formula: see text] is smooth, and [Formula: see text] is a local complete intersection inside [Formula: see text]. We also prove that the canonical model of a rational monomial curve with just one singular point lies on a surface scroll if and only if the gonality of the curve is at most [Formula: see text], and that it lies on a threefold scroll if and only if the gonality is at most [Formula: see text].

scholarly journals The final log canonical model ofℳ6

2014 ◽  
Vol 8 (5) ◽  
pp. 1113-1126 ◽  
Author(s):  
Fabian Müller
Keyword(s):  
Canonical Model ◽  
Log Canonical

scholarly journals Hyperbolicity for Log Smooth Families with Maximal Variation

2021 ◽  
Author(s):  
Chuanhao Wei ◽  
Lei Wu
Keyword(s):  
Open Subset ◽  
Minimal Model ◽  
General Type ◽  
Canonical Model ◽  
Base Space ◽  
Zariski Open Subset ◽  
Smooth Family ◽  
Log Canonical ◽  
The Family

Abstract We prove that the base space of a log smooth family of log canonical pairs of log general type is of log general type as well as algebraically degenerate, when the family admits a relative good minimal model over a Zariski open subset of the base and the relative log canonical model is of maximal variation.

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