Abstract.
The maximal Seshadri number μ(L) of an ample line bundle L on a smooth projective variety X measures the local positivity of the line bundle L at a general point of X. By refining the method of Ein-Küchle-Lazarsfeld, lower bounds on μ(L) are obtained in terms of L n, n=dim(X), for a class of varieties. The main idea is to show that if a certain lower bound is violated, there exists a non-trivial foliation on the variety whose leaves are covered by special curves. In a number of examples, one can show that such foliations must be trivial and obtain lower bounds for μ(L). The examples include the hyperplane line bundle on a smooth surface in ℙ3 and ample line bundles on smooth threefolds of Picard number 1.
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Supported by Grant No. 98-0701-01-5-L from the KOSEF.
Supported by Grant No. KRF-2001-041-D00025 from the KRF.
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Hwang, JM., Keum, J. Seshadri-exceptional foliations. Math. Ann. 325, 287–297 (2003). https://doi.org/10.1007/s00208-002-0377-6
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DOI: https://doi.org/10.1007/s00208-002-0377-6