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Meaning Minimum of Language

For the Supposition of KARCEVSKIJ Sergej

Meaning Minimum of Language

TANAKA Akio

Ocotober 5, 2011

[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 .

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 R of graded ring

is called projective algebraic variety.

Projective algebraic variety is complete.

◊

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]