The algebraic variety of tight frames

Author(s):  
Shayne F. D. Waldron

2012 ◽  
Vol 436 (5) ◽  
pp. 1014-1027 ◽  
Author(s):  
Matthew Fickus ◽  
Dustin G. Mixon ◽  
Janet C. Tremain




2009 ◽  
Vol 157 (6) ◽  
pp. 789-815 ◽  
Author(s):  
V. N. Malozemov ◽  
A. B. Pevnyi


2018 ◽  
Vol 61 (1) ◽  
pp. 166-173
Author(s):  
Cleto B. Miranda-Neto

AbstractIn this note we prove the following surprising characterization: if X ⊂ is an (embedded, non-empty, proper) algebraic variety deûned over a field k of characteristic zero, then X is a hypersurface if and only if the module of logarithmic vector fields of X is a reflexive -module. As a consequence of this result, we derive that if is a free -module, which is shown to be equivalent to the freeness of the t-th exterior power of for some (in fact, any) t ≤ n, then necessarily X is a Saito free divisor.



2015 ◽  
Author(s):  
Matthew Fickus ◽  
John Jasper ◽  
Dustin Mixon ◽  
Jesse Peterson


1953 ◽  
Vol 49 (3) ◽  
pp. 386-396 ◽  
Author(s):  
D. G. Northcott

The recent progress of modern algebra in analysing, from the algebraic standpoint, the foundations of algebraic geometry, has been marked by the rapid development of what may be called ‘analytic algebra’. By this we mean the topological theories of Noetherian rings that arise when one uses ideals to define neighbourhoods; this includes, for instance, the theory of power-series rings and of local rings. In the present paper some applications are made of this kind of algebra to some problems connected with the notion of a branch of a variety at a point.



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