2013 Fiscal Year Final Research Report
Study on Minkowski sums of lattice polytoped and toric varieties
| Project/Area Number |
23540038
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Tohoku University |
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Principal Investigator |
OGATA Shoetsu 東北大学, 理学(系)研究科(研究院), 准教授 (90177113)
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| Co-Investigator(Renkei-kenkyūsha) |
ISHIDA Masanori 東北大学, 大学院・理学研究科, 教授 (30124548)
HARA Nobuo 東京農工大学, 工学研究院, 教授 (90298167)
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| Project Period (FY) |
2011 – 2013
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| Keywords | 代数幾何 |
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| Research Abstract |
The aim of this research is to prove the conjecture that all ample line bundles on a nonsingular toric variety in dimension three and four are normally generated.
In 2011, our article which proves that an ample line bundle on a nonsingular toric 3-fold whose adjoint bundle is not big is normally generated has been printed in a scientific journal. We construct examples of very ample but not normal lattice polytopes in all dimensions greater than two. And we proves that all ample line bundles on a nonsingular toric 3-fold which has a surjective morphism onto the projective line are normally generated. In 2013, we proves that all ample lines bundles on a polarized toric 3-fold which has an ample line bundle with non-big adjoint bundle are normally generated.
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