| Budget Amount *help |
¥13,000,000 (Direct Cost: ¥10,000,000、Indirect Cost: ¥3,000,000)
Fiscal Year 2015: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2014: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2013: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2012: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2011: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
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| Outline of Final Research Achievements |
We studied the holomorphic torsion invariant of 2-elementary K3 surfaces and we determined its explicit formula as a function on the moduli space. It turned out that, for all topological types of involutions, the holomorphic torsion invariant is expressed as the product of an explicit Borcherds product and theta constants.
We also studied the BCOV invariant of Calabi-Yau threefolds and we determined its explicit formula as a function on the moduli space for Borcea-Voisin threefolds. We introduced BCOV invariants for Calabi-Yau orbifolds and made comparison of BCOV invariants between Borcea-Voisin orbifolds and their crepant resolution.
We studied the Borcherds Phi-function and obtained its algebraic expression. Namely, the value of the Borcherds Phi-function at the period of an Enriques surface is expressed as the product of its period and the resultant of its defining equation. As a by-product, we obtained an infinite product expression of theta constants of genus 2.
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