2002 Fiscal Year Final Research Report Summary
The Study of the moduli space of Riemann surfaces and the projective invariants
Project/Area Number 
13640051

Research Category 
GrantinAid for Scientific Research (C)

Allocation Type  Singleyear Grants 
Section  一般 
Research Field 
Algebra

Research Institution  Tsuruoka National College of Technology 
Principal Investigator 
UEMATSU Kazuhiro Tsuruoka National College of Technology, Mechanical Engineering, Associate Professor, 機械工学科, 助教授 (00280339)

Project Period (FY) 
2001 – 2002

Keywords  Abelian conformal field Theory / Fermion / Moduli space / Projective invariants / Schur Polynomials 
Research Abstract 
We tried to clarify the relations between the ring of projective invariants of algebraic curves and the coordinates or the automorphic forms of the moduli space Ag of abelian varieties. But we have had no new results even in the case of g=3. We will continue this research. On the other hand, we have studied the abelian conformal field theory of Npointed Riemann surfaces with Professor Ueno Kenji at Kyoto University because this study may give some information of the moduli space. We defined the complex vector space, which is named the abelian conformal block of an Npointed Riemann surface by the two conditions. We tried to prove that the dimension of conformal block of any Npointed Riemann surface is one. If we succeed, we can define the line bundle on the moduli space of Npointed Riemann surfaces. But we were not able to prove this. There was a little gap. Then by reducing the two gauge conditions to one, we tried to reconstruct the abelian conformal field theory, but we have not finished yet. In the study of abelian conformal field theory we construct the fermion operators acting on the polynomial ring with infinite indeterminants as differential operators. By proving the identities among Schur polynomials or differential polynomials, we directly showed that these operators satisfy the fermion relations. Now we attempt to generalize these relations and find new formula.

Research Products
(2 results)