scholarly journals A numerical condition for a deformation of a Gorenstein surface singularity to admit a simultaneous log-canonical model

2001 ◽  
Vol 129 (10) ◽  
pp. 2823-2831
Author(s):  
Tomohiro Okuma
Keyword(s):  
Canonical Model ◽  
Surface Singularity ◽  
Log Canonical

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.

SIMULTANEOUS GOOD RESOLUTIONS OF DEFORMATIONS OF GORENSTEIN SURFACE SINGULARITIES

2001 ◽  
Vol 12 (01) ◽  
pp. 49-61
Author(s):  
TOMOHIRO OKUMA
Keyword(s):  
Number Field ◽  
Complex Number ◽  
Small Deformation ◽  
Surface Singularity ◽  
Exceptional Sets ◽  
Simultaneous Resolution ◽  
Log Canonical ◽  
Surface Singularities ◽  
Complex Number Field

Let π: X → T be a small deformation of a normal Gorenstein surface singularity X0 over the complex number field [Formula: see text]. We assume that X0 is not log-canonical. Then we prove that if the invariant -Pt · Pt of Xt is constant, then π admits a simultaneous resolution f: M → X such that each ft: Mt → Xt is a smallest resolution among all resolutions of Xt whose exceptional sets are divisors having only normal crossings.

scholarly journals Explicit Models for Threefolds Fibred by K3 Surfaces of Degree Two

2013 ◽  
Vol 65 (4) ◽  
pp. 905-926
Author(s):  
Alan Thompson
Keyword(s):  
K3 Surfaces ◽  
Canonical Model ◽  
Log Canonical ◽  
Small Set

AbstractWe consider threefolds that admit a fibration by K3 surfaces over a nonsingular curve, equipped with a divisorial sheaf that defines a polarization of degree two on the general fibre. Under certain assumptions on the threefold we show that its relative log canonical model exists and can be explicitly reconstructed from a small set of data determined by the original fibration. Finally, we prove a converse to this statement: under certain assumptions, any such set of data determines a threefold that arises as the relative log canonical model of a threefold admitting a fibration by K3 surfaces of degree two.

scholarly journals The Newton tree: geometric interpretation and applications to the motivic zeta function and the log canonical threshold

2015 ◽  
Vol 159 (3) ◽  
pp. 481-515 ◽  
Author(s):  
PIERRETTE CASSOU-NOGUÈS ◽  
WILLEM VEYS
Keyword(s):  
Zeta Function ◽  
Newton Polygon ◽  
Geometric Interpretation ◽  
Canonical Model ◽  
Newton Polygons ◽  
Log Canonical Threshold ◽  
Newton Algorithm ◽  
Log Canonical ◽  
Motivic Zeta Function ◽  
The Ideal

AbstractLet${\mathcal I}$be an arbitrary ideal in${\mathbb C}$[[x,y]]. We use the Newton algorithm to compute by induction the motivic zeta function of the ideal, yielding only few poles, associated to the faces of the successive Newton polygons. We associate a minimal Newton tree to${\mathcal I}$, related to using good coordinates in the Newton algorithm, and show that it has a conceptual geometric interpretation in terms of the log canonical model of${\mathcal I}$. We also compute the log canonical threshold from a Newton polygon and strengthen Corti's inequalities.

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.

A canonical model of migration to cities

1985 ◽  
Vol 3 (1) ◽  
pp. 54-61
Author(s):  
Shekhar Mukherji
Keyword(s):  
Canonical Model
Sign in / Sign up

Export Citation Format

Share Document