| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Outline of Final Research Achievements |
We studied the relation between the embedding structute of projective varieties and their defining equations. For a projective variety X, a point of the projective space is called a nonbirational center of X if the linear projection from it induces a nonbirational map onto its image. By B(X) and C(X), we denote the set of nonbirational centers outside of X and inside of X respectively. We call B(X) and C(X) Segre locus and inner Segre locus respectively. In this study, first we give a characterization of a projective variety X with nonempty B(X) and C(X). As one of applications of this result, we have improved the result on Castelnuovo-Mumford regularity for smooth X of codimension e and degree d by showing that the regularity is at most e(d-e)+1. Second we show that the Castelnuovo-Mumford regularity of X with 1-dimensional C(X) is at most d-e+1. Moreover, as an application of these studies, we have a result of maximal minors of a matrix with homogeneous linear forms as entries.
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