2005 Fiscal Year Final Research Report Summary
Study of modulimap of degenerate families of algebraic curves and local signature arizing from automorphic form
| Project/Area Number |
16540036
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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 | Tohoku-Gakuin University |
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Principal Investigator |
ASHIKAGA Tadashi Tohoku-Gakuin University, Faculty of Engineering, Professor, 工学部, 教授 (90125203)
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| Co-Investigator(Kenkyū-buntansha) |
TUCHIHASHI Hiroyasu Tohoku-Gakuin University, Faculty of General Education, Associated Professor, 教養学部, 助教授 (00146119)
KONNO Kazuhiro Graduate School of Osaka University, Institute of Science, Professor, 大学院・理学研究科, 教授 (10186869)
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| Project Period (FY) |
2004 – 2005
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| Keywords | Algebraic curve / Degenerate family / Signature / Dedekind sum / Stable roduction / Monodromy / Horikawa index / Moduli |
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| Research Abstract |
In 2005, we have the following development about the local signature and Horikawa index of degenerate families of algebraic curves :
(1)The case of stable family ; We have already found in 2004 an application of Harris-Mamford formula to maximal-gonal fibration of addgeues. In 2005, We have found a similar application of Eisenbud-Harris formula to even genus case. More precisely, in the case of genus 4, we obtain a formula for local contribution from the Cheu-Konno lower bound But in the case of genus greater than or equal 6, some difficulties remain, because we need more Sharp form of Eisenbud-Harris formula.
(2)The case of unstable family ; We have already describe in 2004 the behavionr of invariants under the stable reduction by using the Dedekind sam of monodromy data In 2005, we have obtained completely explicite formula for there Dedeking sum tern Therefore we can rewrite out previous formula in a simple form so that the induction with respect to the genus in possible. It seems to be interesting from the number theoretic viewpoint.
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