Bibliography 2011 / Algebraic Geometry

Bibliography 2011
Algebraic Geometry

[CLE-KOL1995] Herbert Clemens, Janos Kollar. Current Topics in Complex Algebraic Geometry. Cambridge University Press, Cambridge, 1995.
[COR2007] Alessio Corti. Flips for 3-folds and 4-folds. Oxford University Press, Oxford, 2007.
[HIR2004] HIRONAKA Hesuke. Algebraic Geometry. Kyoto University Press, Kyoto, 2004.
[IIT2001] IITAKA Shigeru. Geometry of Plane Curve. Kyoritsu Shuppan, Tokyo, 2001.
[ISH2000] ISHIDA Masanori. Basis of Algebraic Geometry. Baifukan, Tokyo, 2000
[KAT1998] KATSURA Toshiyuki. Algebraic Geometry Primer. Kyoritsu Shuppan, Tokyo, 1998.
[KAWAGUCHI2011] KAWAGUCHI Shu. Book review MORIWAKI Atsushi : Arakelov Geometry, Sugaku, January 2011. Iwanami Shoten, 2011.
[KAWAMATA2001] KAWAMATA Yujiro. Geometry of Objective Space. Asakura Shoten, Tokyo, 2001.
[KOL-MOR2008] Janos Kollar, MORI Shigefumi.Birational Geometry. Iwanami Shoten, Tokyo, 2008.
[KON2008] KONO Toshitake. Field Theort and Geometry. Iwanami Shoten, Tokyo, 2008.
[KON2009] KONO Toshitake. Geometry of Repeated Integral. Springer-Japan, Tokyo, 2009.
[KON-TAM2008] KONO Akira, TAMAKI Dai. General Cohomology. Iwanami Shoten, Tokyo,2008.
[MORISHITA2009] MORISHITA Masanori. Knot Theory and Prime Number. Springer-Japan, Tokyo, 2009.
[MORIWAKI Atsushi2008] MORIWAKI Atsushi. Arakelov Geometry. Iwanami Shoten, Tokyo, 2008.
[MUK2008] MUKAI Shigeru. Moduli Theory 1. Iwanami Shoten, Tokyo, 2008.
[MUK2008] MUKAI Shigeru. Moduli Theory 2. Iwanami Shoten, Tokyo, 2008.
[NOG2003] NOGUCHI Junjiro. Several Variable Nevanlinna Theory and Diophantine Approximation. Kyoritsu Shuppan, Tokyo, 2003.
[OSH2008] OSHIKA Ken'ichi. Discrete Group. Iwanami Shoten, Tokyo, 2008.
[SAI2009] SAITO Takeshi. Fermat Conjecture. Iwanami Shoten, Tokyo, 2009.
[TANIYAMA1994] TANIYAMA Yutaka. Complete Works of TANIYAMA Yutakaenlarged edition. Nihonhyoronsha, Tokyo, 1994.
[TANIZAKI2002] TANIZAKI Toshiyuki. Lie Algebra and Quantum Group. Kyoritsu Shuppan, Tokyo, 2002.
[UEN2005] UENO Kenji. Algebraic Geometry. Iwanami Shoten, Tokyo, 2005.
[UEN-SHI2008] UENO Kenji, SHIMIZU Yuji. Deformation and Period of Complex Structure. Iwanami Shoten, Tokyo, 2008.

Tokyo

December 19, 2011
Sekinan Research Field of Language

Reversibility of Language​

​

sekinanlogoshome 

​

Floer Homology Language 

TANAKA Akio 

     

​

Note4 

Reversibility of Language​

​

​

1​

Banach space   E,F​

Local L1,p class map that satisfies  : R×S1 → M      L1,p(R×S1, M; li, lj)    ​

Banach manifold     L1,p(R×S1, M; li, lj)​

Tangent space at      L1,p(R×S1, *TM)​

Section of E (R×S1, M; li, lj)         sh​

​

2​

N| is zero order operator.​

​

3​

​

4​

2n dimensional manifold     M​

Tangent space     TM​

Map     JM : TM → TM​

JM° JM = -1​

​

5 is elliptic 

operator over closed manifold S1 . is Fredholm operator.​

​

6​

(Theorem) is reversible.​

​

7​

Concept <memory> on <Mirror Theory / Tokyo June 5, 2004> is defined by   .​

​

​

[References]​

Mirror Theory / Tokyo June 5, 2004​

Mirror Language / Tokyo June 10, 2004​

Guarantee of Language / Tokyo June 12, 2004​

​

​

​

Tokyo June 5, 2009​

Sekinan Research Field of Language

Source:https://writer.zoho.com/public/sekinan/FHLNote4ReversibilityOfLanguage

Tomita’s Fundamental Theorem

von Neumann Algebra 4

Note 1

Tomita’s Fundamental Theorem  

TANAKA Akio

[Theorem]

(1) JNJ = N ’

(2) Δ^itNΔ^-it = N,  ∀t ∈R

[Preparation]

<1 von Neumann Algebra>

von Neumann algebra     *subalgebra satisfies A ’’ = A. 

<1-1 *subalgebra> 

Algebra A that has involution*       *algebra

Element of *algebra     A∈A

When A = A*, A is called self-adjoint.

When A *A= AA*, A is called normal.

When A A*= 1, A is called unitary.

Subset of A     B

B * := B*∈B

When B = B*, B is called self-adjoint set.

Subalgebra of A     B

When B is adjoint set, B is called *subalgebra.

<1-2 involution*>

Involution * over algebra A over C is map * that satisfies next condition.

Map * : A∈A ↦ A*∈A

Arbitrary A, B∈A, λ∈C

(i) (A*)* = A

(ii) (A+B)* = A*+B*

(iii) (λA)* =λ^-A*

(iiii) (AB)* = B*A*

<2 Modular operator, modular conjugation>

Δ is called modular operator on x₀.

J is called modular conjugation on x₀.

<2-1 Modular operator>

Δ = R^-1(2I-R), Δ^it = R^-it(2I-R)^it, t ∈R.

Δis unbounded positive self-adjoint operator.

Δ^it is 1 coefficient unitary group.

<2-2 Modular conjugation>

J is adjoint linear isometric operator, J² = I.

<2-3 Symmetric operator>

Objection operator from H_R to K, iK     P, Q

R = P + Q

Polar decomposition of P - Q at H_R     P – Q = JT

T is positive symmetric operator over H_R.

Re<x, Ty> = Re<Tx, y>

T² = (P – Q)²

<2-4 Polar decomposition>

φ∈N_*, ψ∈N_*,+

Partial isometric operator     V∈N

φ = R_Vψ and V*V = s(ψ)

|| φ|| = || ψ ||

ψ is called absolute value ofφ.

φ = R_Vψ is called polar decomposition ofφ.

<2-5 N_* >

Bounded linear functional over N     N_*

To be continued

Tokyo May 3, 2008

Sekinan Research Field of Language

www.sekinan.org

[Postscript August 2, 2008]

<On [Theorem] (1) JNJ = N ’>

Algebraic Linguistics / Linguistic Result / Deep Fissure between Word and Sentence / Tokyo September 10, 2007

von Neumann Algebra 4 / Conjecture 1 / Relation between Word and Sentence / Tokyo May 5, 2008

<For more details>

Case

Theorem / Eliashberg​, Tomita, Borchers

Symplectic Language Theory 

TANAKA Akio 

     

​

Note 1 

Symplectic Topological Existence Theorem​

​

​

[Theorem]​

(Eliashberg)​

Symplectic homeomorphism   is C0 convergent to differential 

homeomorphism .​

Under the upper condition, φ is symplectic homeomorphism.​

​

​

[Note]​

1​

For language's understandability, differential homeomorphic C0 convergence is related with 

the finiteness and infinity of language. ​

2​

For the finiteness and infinity of language, next theorem is eficient to solve the problem.​

​

(Tomita's fundamental theorem)​

H       Hilbert space        ​

B(H)  Banach space B(H, H)​

N       B(H)'s *subalgebra that contains identity operator and closes for τuw topology​

J        Conjugate linear equidistance operator​

Δ       Unbounded positive self-adjoint operator​

Δit     τs-continuous 1 parameter unitary group​

(1) ​

(2) ​

​

(Borchers' theorem 1992)​

The theorem is deeply connected with Tomita's theorem.​

​

​

[Impression]​

Symplectic geometric structure is seemed to be solvable for language's understandability that 

simultaneously connotes finiteness and infinity within. ​

​

​

[References]​

<Topological approach>​

#1 Topological Approach​

<Language's understandability>​

#2 Deep Fissure between Word and Sentence​

#3 Finiteness in Infinity on Language​

<Related theorems>​

#4 Tomita's Fundamental Theorem​

#5 Borchers' Theorem​

<Related twitter site>​

#6 sekinanlu​

​

​

​

To be continued​

Tokyo February 27, 2009​

Sekinan Research Field of language​

Source:

  

   
                   https://writer.zoho.com/public/sekinan/SLTNote1SymplecticTopologicalExistenceTheorem1