general orbit
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Author(s):  
ELEONORA A. ROMANO ◽  
JAROSŁAW A. WIŚNIEWSKI

Abstract Let X be a complex projective manifold, L an ample line bundle on X, and assume that we have a ℂ* action on (X;L). We classify such triples (X; L;ℂ*) for which the closure of a general orbit of the ℂ* action is of degree ≤ 3 with respect to L and, in addition, the source and the sink of the action are isolated fixed points, and the ℂ* action on the normal bundle of every fixed point component has weights ±1. We treat this situation by relating it to the classical adjunction theory. As an application, we prove that contact Fano manifolds of dimension 11 and 13 are homogeneous if their group of automorphisms is reductive of rank ≥ 2.



Author(s):  
Harold L. Hallock ◽  
Gary Welter ◽  
David G. Simpson ◽  
Christopher Rouff
Keyword(s):  


2012 ◽  
Vol 45 (4) ◽  
pp. 834-837
Author(s):  
Leopoldo Suescun ◽  
Massimo Nespolo

The space group of a crystal pattern is the intersection group of the eigensymmetries of the crystallographic orbits corresponding to the occupied Wyckoff positions. Polar space groups without symmetry elements with glide or screw components smaller than 1/2 do not contain characteristic orbits and cannot be realized in patterns (structures) made by only one crystallographic type of object (atom). The space-group diagram of the general orbit for this type of group has an eigensymmetry that corresponds to a special orbit in a centrosymmetric supergroup of the generating group. This fact is often overlooked, as shown in the proposed solution for Plates (i)–(vi) of IUCr Teaching Pamphlet No. 14, and an alternative interpretation is given.



1980 ◽  
Vol 171 (3) ◽  
pp. 439-443
Author(s):  
W.M. Schulte ◽  
H.L. Hagedoorn


1979 ◽  
Author(s):  
L.B. Maddox ◽  
G.S. McNeilly
Keyword(s):  


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