Birational equivalence of tori with a cyclic splitting field

1981 ◽  
Vol 17 (2) ◽  
pp. 1819-1823 ◽  
Author(s):  
A. L. Chistov
Keyword(s):  
Splitting Field ◽  
Birational Equivalence

scholarly journals Colloquium : Nonequilibrium effects in superconductors with a spin-splitting field

2018 ◽  
Vol 90 (4) ◽  
Author(s):  
F. Sebastian Bergeret ◽  
Mikhail Silaev ◽  
Pauli Virtanen ◽  
Tero T. Heikkilä
Keyword(s):  
Splitting Field ◽  
Spin Splitting ◽  
Nonequilibrium Effects

Polynomials with Certain Prescribed Conditions on the Galois Group

1969 ◽  
Vol 21 ◽  
pp. 262-273 ◽  
Author(s):  
Elizabeth Rowlinson ◽  
Hans Schwerdtfeger
Keyword(s):  
Nilpotent Group ◽  
Galois Group ◽  
Canonical Form ◽  
Nilpotent Groups ◽  
Faithful Representation ◽  
Splitting Field ◽  
Normal Extension ◽  
Algebraic Equations ◽  
Abstract Group ◽  
Group A

In this paper, some contributions are made to the theory of algebraic equations over the rational field with conditions imposed on the Galois group. In § 1, for a given abstract group G all faithful permutation representations Ḡ are obtained, and it is shown that if one of them is the group of some equation with splitting field K, then any of them is the group of some equation, also with splitting field K. The method of proof enables us to construct an equation having as group a given faithful permutation representation Ḡ of a prescribed group G if we are given an equation having as group some faithful representation of G. In § 2, equations having nilpotent group are considered, non-normal extension fields are discussed, and a canonical form is obtained for the roots of non-normal irreducible equations; this form is used to characterize fields and equations with nilpotent groups.

scholarly journals MINIMAL MODEL PROGRAM WITH SCALING AND ADJUNCTION THEORY

2013 ◽  
Vol 24 (02) ◽  
pp. 1350007 ◽  
Author(s):  
MARCO ANDREATTA
Keyword(s):  
Minimal Model ◽  
Projective Variety ◽  
Model Program ◽  
Minimal Model Program ◽  
Projective Varieties ◽  
Complex Projective Variety ◽  
Adjunction Theory ◽  
Birational Equivalence ◽  
Big Line Bundle ◽  
Complex Projective

Let (X, L) be a quasi-polarized pair, i.e. X is a normal complex projective variety and L is a nef and big line bundle on it. We study, up to birational equivalence, the positivity (nefness) of the adjoint bundles KX + rL for high rational numbers r. For this we run a Minimal Model Program with scaling relative to the divisor KX + rL. We give then some applications, namely the classification up to birational equivalence of quasi-polarized pairs with sectional genus 0, 1 and of embedded projective varieties X ⊂ ℙN with degree smaller than 2 codim ℙN(X) + 2.

Study on a Controlled Splitting Scheme Based on Layer Expanding Graph Algorithm

2014 ◽  
Vol 577 ◽  
pp. 974-977
Author(s):  
Jian Yang ◽  
Fei Tang ◽  
Qing Fen Liao ◽  
Yi Fei Wang
Keyword(s):  
Power System ◽  
Operation Mode ◽  
Graph Algorithm ◽  
Splitting Field ◽  
Splitting Scheme ◽  
Simulation Results ◽  
Bus System

Optimal controlled splitting is an emergency strategy to split the power system into several sub-regions based on global electrical information before the collapse of the system which is subject to severe disturbances. How to seek the optimal splitting sections rapidly and accurately is a key problem in controlled splitting field. A controlled splitting scheme based on layer expanding graph algorithm is presented in this paper. Firstly, source nodes of island regions extend out for the formation of the island regions. Secondly, island regions can be combined to make up synchronous sub-regions on the basis of the clustering of generators. At last, the optimal sections can be determined according to the initial and improved adjustment of splitting sections. Moreover, the scheme proposed can be adapt to the change of operation mode of the power system. The accuracy and effectiveness of the scheme is shown by the simulation results of CEPRI 36-bus system.

scholarly journals CHARACTER VARIETIES OF ONCE-PUNCTURED TORUS BUNDLES WITH TUNNEL NUMBER ONE

2013 ◽  
Vol 24 (06) ◽  
pp. 1350048 ◽  
Author(s):  
KENNETH L. BAKER ◽  
KATHLEEN L. PETERSEN
Keyword(s):  
Boundary Component ◽  
Lens Space ◽  
Algebraic Sets ◽  
Character Varieties ◽  
Torus Bundles ◽  
Whitehead Link ◽  
Birational Equivalence ◽  
Punctured Torus ◽  
Tunnel Number ◽  
Trace Fields

We determine the PSL2(ℂ) and SL2(ℂ) character varieties of the once-punctured torus bundles with tunnel number one, i.e. the once-punctured torus bundles that arise from filling one boundary component of the Whitehead link exterior. In particular, we determine "natural" models for these algebraic sets, identify them up to birational equivalence with smooth models, and compute the genera of the canonical components. This enables us to compare dilatations of the monodromies of these bundles with these genera. We also determine the minimal polynomials for the trace fields of these manifolds. Additionally, we study the action of the symmetries of these manifolds upon their character varieties, identify the characters of their lens space fillings, and compute the twisted Alexander polynomials for their representations to SL2(ℂ).

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