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

Research Category 
GrantinAid for Scientific Research (C)

Allocation Type  Singleyear Grants 
Section  一般 
Research Field 
Algebra

Research Institution  TohokuGakuin University 
Principal Investigator 
ASHIKAGA Tadashi TohokuGakuin University, Faculty of Engineering, Professor, 工学部, 教授 (90125203)

CoInvestigator(Kenkyūbuntansha) 
TUCHIHASHI Hiroyasu TohokuGakuin 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)

Project Period (FY) 
2004 – 2005

Keywords  Algebraic curve / Degenerate family / Signature / Dedekind sum / Stable roduction / Monodromy / Horikawa index / Moduli 
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 HarrisMamford formula to maximalgonal fibration of addgeues. In 2005, We have found a similar application of EisenbudHarris formula to even genus case. More precisely, in the case of genus 4, we obtain a formula for local contribution from the CheuKonno lower bound But in the case of genus greater than or equal 6, some difficulties remain, because we need more Sharp form of EisenbudHarris 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.

Research Products
(2 results)