2013 Fiscal Year Final Research Report
Studies of families of rational curves and characterizations of homogeneous manifolds
| Project/Area Number |
24840008
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | Saitama University |
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Principal Investigator |
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| Research Collaborator |
MUÑOZ Roberto Universidad Rey Juan Carlos
OCCHETTA Gianluca Università di Trento
CONDE Luis E. Solá Universidad Rey Juan Carlos, KIAS
J. Wiśniewski Uniwersytet Warszawski
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| Project Period (FY) |
2012-08-31 – 2014-03-31
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| Keywords | ファノ多様体 / ネフ接束 / 等質多様体 |
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| Research Abstract |
I have studied Fano manifolds with nef tangent bundles. It is conjectured that such manifolds are rational and homogeneous by Campana and Peternell, which is called the CP conjecture. First, I proved that the conjecture holds for Fano 5-folds of Picard number >1. The result was published from Math Zeitsherift. On the other hand, I studied some problems related to the CP conjecture with R. Munoz, G. Occhetta, L. Sola Conde and J. Wiśniewski. In particular, we proved that Fano manifolds whose elementary contractions are smooth P1-fibrations are complete flag manifolds. As a corollary, the CP conjecture can be boiled down to another problem. We wrote two papers on this topic and these papers are submitted.
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