Seshadri constants and degrees of defining polynomials
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In this paper, we study a relation between Seshadri constants and degrees of defining polynomials. In particular, we compute the Seshadri constants on Fano varieties obtained as complete intersections in rational homogeneous spaces of Picard number one.
Mathematics Subject Classification (1991)14C20
The authors would like to express their gratitude to Professor Yujiro Kawamata for his valuable advice, comments, and warm encouragement. They are also grateful to Professors Katsuhisa Furukawa and Kiwamu Watanabe for their useful comments and suggestions.
- 3.Debarre, O.: Higher-dimensional algebraic geometry, Universitext, pp. xiv+233. Springer, New York (2001)Google Scholar
- 4.Demailly, J.P.: Singular Hermitian metrics on positive line bundles, complex algebraic varieties (Bayreuth, 1990), Lecture Notes in Math., vol. 1507, pp. 87–104. Springer, Berlin (1992)Google Scholar
- 6.Ito, A.: Seshadri constants via toric degenerations. J. Reine Angew. Math. doi: 10.1515/crelle-2012-0116 (2012, to appear)
- 7.Kollár, J.: Rational curves on algebraic varieties, Ergeb. Math. Grenzgeb. (3), vol. 32, Springer, Berlin (1996)Google Scholar
- 8.Lazarsfeld, R.: Positivity in algebraic geometry I, Ergebnisse der Mathematik undihrer Grenzgebiete, vol. 48. Springer, Berlin (2004)Google Scholar
- 10.Mumford, D.: Varieties defined by quadratic equations, 1970 Questions on Algebraic Varieties (C.I.M.E., III Ciclo, Varenna, 29–100 Edizioni Cremonese, Rome (1969)Google Scholar