Pseudofree ℤ/3-actions on elliptic surfaces E (4)

2008 ◽  
Vol 45 (2) ◽  
pp. 273-284 ◽  
Author(s):  
Hongxia Li ◽  
Ximin Liu
Keyword(s):  
Cyclic Group ◽  
Elliptic Surface ◽  
Elliptic Surfaces ◽  
Locally Linear

In this paper we give a weak classification of locally linear pseudofree actions of the cyclic group of order 3 on an elliptic surface E (4), and prove the existence of such actions which can not be realized as smooth actions on the standard smooth E (4).

scholarly journals Corrigenda On a classification of the function fields of algebraic tori: (Nagoya Math. J. 56 (1975), 85–104)

1980 ◽  
Vol 79 ◽  
pp. 187-190 ◽  
Author(s):  
Shizuo Endo ◽  
Takehiko Miyata
Keyword(s):  
Direct Product ◽  
Cyclic Group ◽  
Prime Divisor ◽  
Dihedral Group ◽  
Quaternion Group ◽  
Algebraic Tori ◽  
Root Of Unity ◽  
Generalized Quaternion Group ◽  
Generalized Quaternion

There are some errors in Theorems 3.3 and 4.2 in [2]. In this note we would like to correct them.1) In Theorem 3.3 (and [IV]), the condition (1) must be replaced by the following one;(1) П is (i) a cyclic group, (ii) a dihedral group of order 2m, m odd, (iii) a direct product of a cyclic group of order qf, q an odd prime, f ≧ 1, and a dihedral group of order 2m, m odd, where each prime divisor of m is a primitive qf-1(q — 1)-th root of unity modulo qf, or (iv) a generalized quaternion group of order 4m, m odd, where each prime divisor of m is congruent to 3 modulo 4.

scholarly journals FIBER PRODUCTS OF ELLIPTIC SURFACES WITH SECTION AND ASSOCIATED KUMMER FIBRATIONS

2009 ◽  
Vol 20 (04) ◽  
pp. 401-426 ◽  
Author(s):  
GRZEGORZ KAPUSTKA ◽  
MICHAŁ KAPUSTKA
Keyword(s):  
Elliptic Surfaces ◽  
Singular Fibers ◽  
Hodge Numbers

We investigate Calabi–Yau three folds which are small resolutions of fiber products of elliptic surfaces with section admitting reduced fibers. We start by the classification of all fibers that can appear on such varieties. Then, we find formulas to compute the Hodge numbers of obtained three folds in terms of the types of singular fibers of the elliptic surfaces. Next, we study Kummer fibrations associated to these fiber products.

Automated, rapid classification of signals using locally linear embedding

2011 ◽  
Vol 38 (10) ◽  
pp. 13472-13474 ◽  
Author(s):  
J.M. Nichols ◽  
F. Bucholtz ◽  
B. Nousain
Keyword(s):  
Locally Linear Embedding ◽  
Linear Embedding ◽  
Locally Linear

scholarly journals The Nef Cone of the Hilbert Scheme of Points on Rational Elliptic Surfaces and the Cone Conjecture

2020 ◽  
pp. 1-12
Author(s):  
John Kopper
Keyword(s):  
Hilbert Scheme ◽  
Elliptic Surface ◽  
Elliptic Surfaces ◽  
Hilbert Scheme Of Points ◽  
Rational Elliptic Surfaces ◽  
Nef Cone ◽  
Rational Elliptic Surface

Abstract We compute the nef cone of the Hilbert scheme of points on a general rational elliptic surface. As a consequence of our computation, we show that the Morrison–Kawamata cone conjecture holds for these nef cones.

scholarly journals Generalized Fibonacci groups H(r,n,s) that are connected labelled oriented graph groups

2019 ◽  
Vol 22 (1) ◽  
pp. 23-39 ◽  
Author(s):  
Gerald Williams
Keyword(s):  
Cyclic Group ◽  
Betti Numbers ◽  
Oriented Graph ◽  
Complete Classification ◽  
Circulant Matrices ◽  
Fundamental Groups ◽  
Infinite Cyclic Group ◽  
Torus Knot ◽  
Graph Groups

Abstract The class of connected Labelled Oriented Graph (LOG) groups coincides with the class of fundamental groups of complements of closed, orientable 2-manifolds embedded in {S^{4}} , and so contains all knot groups. We investigate when Campbell and Robertson’s generalized Fibonacci groups {H(r,n,s)} are connected LOG groups. In doing so, we use the theory of circulant matrices to calculate the Betti numbers of their abelianizations. We give an almost complete classification of the groups {H(r,n,s)} that are connected LOG groups. All torus knot groups and the infinite cyclic group arise and we conjecture that these are the only possibilities. As a corollary we show that {H(r,n,s)} is a 2-generator knot group if and only if it is a torus knot group.

scholarly journals On the faithful representations, of degree 2n, of certain extensions of 2-groups by orthogonal and symplectic groups

1995 ◽  
Vol 58 (2) ◽  
pp. 232-247 ◽  
Author(s):  
S. P. Glasby
Keyword(s):  
Cyclic Group ◽  
Projective Representation ◽  
Faithful Representation ◽  
Explicit Description ◽  
Symplectic Groups ◽  
Classical Groups ◽  
Central Extensions ◽  
Central Product ◽  
Extraspecial Group

AbstractIf R is a 2-group of symplectic type with exponent 4, then R is isomorphic to the extraspecial group , or to the central product 4 o 21+2n of a cyclic group of order 4 and an extraspecial group, with central subgroups of order 2 amalgamated. This paper gives an explicit description of a projective representation of the group A of automorphisms of R centralizing Z(R), obtained from a faithful representation of R of degree 2n. The 2-cocycle associated with this projective representation takes values which are powers of −1 if R is isomorphic to and powers of otherwise. This explicit description of a projective representation is useful for computing character values or computing with central extensions of A. Such central extensions arise naturally in Aschbacher's classification of the subgroups of classical groups.

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