| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2019: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2018: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2017: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Outline of Final Research Achievements |
We studied the relation between the embedding structure of projective varieties and their defining ideal. For a projective variety, its double point divisor is the nonisomorphic locus of the variety by the inner projection from the linear subspace spanned by its general (e-1)-points to its image. On the other hand, a nonbirational center of a projective variety is a point from which the variety is projected nonisomorphically. The locus of nonbirational centers off the variety (resp. on its smooth locus) is called outer (resp. Inner) Segre locus of the variety. We get the following two results. The first result is to show that the linear subsystem consisting of double point divisors of a projective variety has the base points in the singular locus or the inner Segre locus of the variety. The second result is to give upper bounds of the number of irreducible components of the Segre locus of a projective variety by its degree, dimension and codimension.
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