Period integral of algebraic varieties
Grant-in-Aid for Scientific Research (C)
|Allocation Type||Single-year Grants |
|Research Institution||The University of Tokyo |
TERASOMA Tomohide The University of Tokyo, Garduate School of Mathematical Sciences, Professor (50192654)
OGISO Keiji Keio University, Faculty of Economics, Professor (40224133)
YOSHIKAWA Ken-ichi The University of Tokyo, Graduate School of Mathematical Sciences, Associate Professor (20242810)
HOSONO Shinobu The University of Tokyo, Graduate School of Mathematical Sciences, Associate Professor (60212198)
MATSUMOTO Keiji Hokkaido University, Graduate School of Science, Associate Professor (30229546)
|Project Period (FY)
2004 – 2007
Completed (Fiscal Year 2007)
|Budget Amount *help
¥3,840,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥240,000)
Fiscal Year 2007: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2006: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2005: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2004: ¥900,000 (Direct Cost: ¥900,000)
|Keywords||motif / bar construction / arithmetic geometric mean / Hodge structures / 周期積分 / 多重ゼータ値|
(1) We define a homomorphism from the polylog complex defined by Goncharov to the extension group of mixed Tate motives defined by Bloch and Kriz. The existence of this map is conjectured by Beilinson-Deligne. Beilinson and Deligne assume some conjectures which are equivalent to the KP1 conjecture and Beilinson-Soule conjecture. We constructed the homomorphism without assuming these conjecture using bar constructions and recovery principle for them.
(2) We show the differential graded category equivalence between the category of comodules of differential graded Hopf algebra and that of differential graded complex over differential graded category associated a differential graded algebra Using this equivalence, we showed that the Hopf coalgebra constructed form the Deligne algebra classifies the category of variation of mixed Tate Hodge structures.
(3) We give a description of the pro-p completion of algebraic varieties of positive characteristic, which classifies the Tannakian category o
f Fp local systems in terms of Bar constructions. To get a product structure on the corresponding Hopf algebra, we introduce a homotopy shuffle product. Via this shuffle product, we get a notion of group like elements which give the description of pro-p completion.
(4) We define arithmetic-geometric mean for hyperelliptic cureves of higher genus, which is a generalization of Gauss arithmetic geometric mean- Moreover, we showed that they coincides with certain determinant of periods of hyperellipitic curves using Thomae's formlula. We showed that this is also equal to a period of certain Calabi-Yau varieties.
(5) We construct certain algebraic correspondence between Jacobian varieties and Calabi-Yau varieties obtained by a double covering of three dimensional projective space branched at the projective dual of Caylay Octad of genus three cureves. More over the third cohomology of the Calabi-Yau varieties are not exterior product in general by looking infinitesimal variation of Hodge structures. Less
Report (5 results)
Research Products (32 results)