Diophantine Language Dimension of Words

Home  »   Papers »  Diophantine Language »  Dimension of Word Diophantine Language Dimension of Words TANAKA Akio [Preparation 1] k is algebraic field. V is non-singular projective algebraic manifold over k. D is reduced divisor over k. Logarithmic irregular index, q (V \ D) =  is supposed. [Theorem, Vojta 1996] Under Preparation 1, for (S,D)-integar subset Z  V (k) \ D, there exists Zariski closed proper subset and there becomes  [Preparation 2] k is algebraic field. V is n-dimensional projective algebraic manifold.  are different reduced divisors each other over V.  . W is (S,D)-integar subset Z  V (k) \ D 's Zariski closuere in V. [Theorem, Noguchi・Winkelmann, 2002] (i) When l ' is the number of different each other, dim W ≥ l ' -r({Di}) + q(W) . (ii) {Di} is supposed to be rich divisor at general location. (l - n) dim W ≤n(r({Di}) - q(W)) + . [Interpretation of Theorem ( Noguchi, Winkelmann)] k is language. V is word. W is meaning. Di is meaning minimum. W has dimension that is defined at sup. or inf. [References] Holomorphic Meaning Theory 2 / Tokyo June 19, 2008 Energy Distance Theory / Conjecture 1 / Word and Meaning Minimum / Tokyo September 22, 2008 Language, Word, Distance, Meaning and Meaning Minimum by Riemann-Roch Formula / Tokyo August 15, 2009 Tokyo January 30, 2012 Sekinan Research Field of Language