| Budget Amount *help |
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2012: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2011: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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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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