The Study of the moduli space of Riemann surfaces and the projective invariants
| Project/Area Number |
13640051
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Tsuruoka National College of Technology |
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Principal Investigator |
UEMATSU Kazuhiro Tsuruoka National College of Technology, Mechanical Engineering, Associate Professor, 機械工学科, 助教授 (00280339)
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| Project Period (FY) |
2001 – 2002
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| Project Status |
Completed (Fiscal Year 2002)
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| Budget Amount *help |
¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2002: ¥300,000 (Direct Cost: ¥300,000)
Fiscal Year 2001: ¥500,000 (Direct Cost: ¥500,000)
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| Keywords | Abelian conformal field Theory / Fermion / Moduli space / Projective invariants / Schur Polynomials / 射影不変量 / 保型形式 |
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| 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 N-pointed 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 N-pointed Riemann surface by the two conditions. We tried to prove that the dimension of conformal block of any N-pointed Riemann surface is one. If we succeed, we can define the line bundle on the moduli space of N-pointed 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.
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Report
(3 results)
Research Products
(4 results)
