scholarly journals ON TORUS ACTIONS OF HIGHER COMPLEXITY

2019 ◽  
Vol 7 ◽  
Author(s):  
JÜRGEN HAUSEN ◽  
CHRISTOFF HISCHE ◽  
MILENA WROBEL
Keyword(s):  
Ring Theory ◽  
Torus Action ◽  
Toric Geometry ◽  
Algebraic Varieties ◽  
Picard Number ◽  
Graded Ring ◽  
Torus Actions ◽  
Rational Varieties ◽  
General Arrangement ◽  
Mori Dream Spaces

We systematically produce algebraic varieties with torus action by constructing them as suitably embedded subvarieties of toric varieties. The resulting varieties admit an explicit treatment in terms of toric geometry and graded ring theory. Our approach extends existing constructions of rational varieties with torus action of complexity one and delivers all Mori dream spaces with torus action. We exhibit the example class of ‘general arrangement varieties’ and obtain classification results in the case of complexity two and Picard number at most two, extending former work in complexity one.

An application of the method of orthogonal completeness in graded ring theory

2013 ◽  
Vol 52 (2) ◽  
pp. 98-104 ◽  
Author(s):  
A. L. Kanunnikov
Keyword(s):  
Ring Theory ◽  
Graded Ring ◽  
Orthogonal Completeness

scholarly journals A software package for Mori dream spaces

2015 ◽  
Vol 18 (1) ◽  
pp. 647-659 ◽  
Author(s):  
Jürgen Hausen ◽  
Simon Keicher
Keyword(s):  
Software Package ◽  
Toric Varieties ◽  
Quotient Singularity ◽  
Algebraic Varieties ◽  
Cox Rings ◽  
Cox Ring ◽  
Mori Dream Spaces ◽  
The Common ◽  
Symplectic Resolutions

Mori dream spaces form a large example class of algebraic varieties, comprising the well-known toric varieties. We provide a first software package for the explicit treatment of Mori dream spaces and demonstrate its use by presenting basic sample computations. The software package is accompanied by a Cox ring database which delivers defining data for Cox rings and Mori dream spaces in a suitable format. As an application of the package, we determine the common Cox ring for the symplectic resolutions of a certain quotient singularity investigated by Bellamy–Schedler and Donten-Bury–Wiśniewski.

Topics in graded ring theory

1979 ◽  
pp. 36-127
Author(s):  
C. Năstăsescu ◽  
F. Van Oystaeyen
Keyword(s):  
Ring Theory ◽  
Graded Ring

scholarly journals Convexity of the moment map image for torus actions on b m -symplectic manifolds

2018 ◽  
Vol 376 (2131) ◽  
pp. 20170420 ◽  
Author(s):  
Victor W. Guillemin ◽  
Eva Miranda ◽  
Jonathan Weitsman
Keyword(s):  
Symplectic Manifold ◽  
Integrable Systems ◽  
Symplectic Manifolds ◽  
Moment Map ◽  
Torus Action ◽  
Convexity Theorem ◽  
Theme Issue ◽  
Torus Actions ◽  
Finite Dimensional ◽  
The Moment

We prove a convexity theorem for the image of the moment map of a Hamiltonian torus action on a b m -symplectic manifold. This article is part of the theme issue ‘Finite dimensional integrable systems: new trends and methods’.

scholarly journals Construction of Free Energy of Calabi–Yau Manifold Embedded in CPN-1 via Torus Actions

1997 ◽  
Vol 12 (32) ◽  
pp. 5775-5802 ◽  
Author(s):  
Masao Jinzenji
Keyword(s):  
Free Energy ◽  
Integral Representation ◽  
Path Integral ◽  
Correlation Functions ◽  
Sigma Model ◽  
Torus Action ◽  
Torus Actions ◽  
Path Integral Representation

We calculate correlation functions of topological sigma model (A-model) on Calabi–Yau hypersurfaces in CPN-1 using torus action method. We also obtain path-integral representation of free energy of the theory coupled to gravity.

scholarly journals Examples of Mori dream spaces with Picard number two

2014 ◽  
Vol 145 (3-4) ◽  
pp. 243-254 ◽  
Author(s):  
Atsushi Ito
Keyword(s):  
Picard Number ◽  
Mori Dream Spaces

scholarly journals UNIFORMLY RATIONAL VARIETIES WITH TORUS ACTION

2017 ◽  
Vol 24 (1) ◽  
pp. 149-153
Author(s):  
ALVARO LIENDO ◽  
CHARLIE PETITJEAN
Keyword(s):  
Torus Action ◽  
Rational Varieties

Some applications of graded ring theory

1986 ◽  
Vol 14 (8) ◽  
pp. 1565-1596
Author(s):  
F. Van Oystaeyen
Keyword(s):  
Ring Theory ◽  
Graded Ring

MAXIMAL TORUS ACTIONS ON SOLVMANIFOLDS AND DOUBLE COSET SPACES

1991 ◽  
Vol 02 (01) ◽  
pp. 67-76
Author(s):  
KYUNG BAI LEE ◽  
FRANK RAYMOND
Keyword(s):  
Lie Groups ◽  
Lie Group ◽  
Maximal Torus ◽  
Double Coset ◽  
Torus Action ◽  
Torus Actions ◽  
Coset Spaces ◽  
Aspherical Manifold ◽  
Aspherical Manifolds ◽  
Connected Lie Group

Any compact, connected Lie group which acts effectively on a closed aspherical manifold is a torus Tk with k ≤ rank of [Formula: see text], the center of π1 (M). When [Formula: see text], the torus action is called a maximal torus action. The authors have previously shown that many closed aspherical manifolds admit maximal torus actions. In this paper, a smooth maximal torus action is constructed on each solvmanifold. They also construct smooth maximal torus actions on some double coset spaces of general Lie groups as applications.

scholarly journals Form rings and regular sequences

1978 ◽  
Vol 72 ◽  
pp. 93-101 ◽  
Author(s):  
Paolo Valabrega ◽  
Giuseppe Valla
Keyword(s):  
Local Ring ◽  
Singular Points ◽  
Point Of View ◽  
Algebraic Varieties ◽  
Associated Graded Ring ◽  
Graded Ring ◽  
Standard Bases ◽  
Regular Sequences ◽  
Initial Forms ◽  
The Ideal

Hironaka, in his paper [H1] on desingularization of algebraic varieties over a field of characteristic 0, to deal with singular points develops the algebraic apparatus of the associated graded ring, introducing standard bases of ideals, numerical characters ν* and τ* etc. Such a point of view involves a deep investigation of the ideal b* generated by the initial forms of the elements of an ideal A of a local ring, with respect to a certain ideal a.

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