Finiteness of Words
[Preparation 1]
k is algebraic field.
is finite subset.
V is projective algebraic manifold over k.
D is defined divisor over k.
All the sub-manifolds are over k.
Rational point is k-rational point.
[Preparation 2]
L is rich line bundle.
|L| is complete linear system.
D is divisor of |L|.
is regular cut to D.
is approximate function to D.
is counting function to D.
is rich line bundle.
When 
islarge, 
becomes rich.
is basis of 
.
is embedding.
[Definition 1]
,
,
.
[Definition 2]
Subset of rational points 
\ 
is 
integer under the next condition.
(i) There exists a certain constant 
.
(ii) 
\ 
.
[Theorem, Faltings]
A is Abelian variety over k.
When D is reduced rich divisor, arbitrary integer subset 
\ is always finite set.
[Interpretation]
D is meaning minimum. \ is word.
A is language.
[References]
From Cell to Manifold / Cell Theory / Tokyo June 2, 2007
Amplitude of Meaning Minimum / Complex Manifold Deformation Theory / Tokyo December 17, 2008
Language, Word, Distance, Meaning and Meaning Minimum by Riemann-Roch Formula / Tokyo August 15, 2009
Tokyo
January 29, 2012
Sekinan Research Field of Language
No comments:
Post a Comment