Thursday, 4 December 2014

Meaning Minimum of Language / 5 October 2011

For the Supposition of KARCEVSKIJ Sergej

Meaning Minimum of Language


[Preparation]
 ,
is graded ring and integral domain.
For negative e .
R's quotient field element is called homogenious when R's quotient field element is ratio f/g of homogenious element  .
Its degree is defined by .
<Definition>
At R's quotient field, subfield made by degree 0's whole homogenious elements,
 ,
is expressed by  .
For homogenious element  ,
subring of field  ,
 ,
is expressed by  .
For graded ring,
 ,
algebraic variety that  is quotient field that whole  for homogenious element  is gotten by gluing in common quotient field is expressed by Proj R.
Proj of graded ring
,
 ,
is called projective algebraic variety.
<Conposition>
Projective algebraic variety is complete.
<System>
Moduli of hypersurface,
,
is complete algebraic variety.
 ,
is sum set of,
 ,  .
[Interpretation]
Word is expressed by,
 .
Meaning minimum of word is expressed by,
 .
For meaning minimum,
refer to the next.
[References]
October 5, 2011

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