# zbMATH — the first resource for mathematics

Seshadri constants on the self-product of an elliptic curve. (English) Zbl 1171.14021
Let $$X$$ be a smooth projective variety of dimension $$n$$ defined over the field of complex numbers and let $$L$$ be an ample line bundle on $$X$$. Then the Seshadri constant $$\varepsilon(L,x)$$ of $$L$$ at $$x$$ is defined by the following: $$\varepsilon(L,x):=\text{sup}\{\epsilon >0\;|\;\text{}f^{*}(L)-\epsilon E$$ is nef

##### MSC:
 14H52 Elliptic curves 14C20 Divisors, linear systems, invertible sheaves 14Jxx Surfaces and higher-dimensional varieties 14Kxx Abelian varieties and schemes
Full Text:
##### References:
 [1] Bauer, Th., Quartic surfaces with 16 skew conics, J. reine angew. math., 464, 207-217, (1995) · Zbl 0826.14020 [2] Bauer, Th., Seshadri constants and periods of polarized abelian varieties, Math. ann., 312, 607-623, (1998) · Zbl 0933.14025 [3] Bauer, Th.; Szemberg, T., Seshadri constants on abelian surfaces, Math. ann., 312, 607-623, (1998), Appendix to: Th. Bauer, Seshadri constants and periods of polarized abelian varieties · Zbl 0933.14025 [4] Bauer, Th., Seshadri constants on algebraic surfaces, Math. ann., 313, 547-583, (1999) · Zbl 0955.14005 [5] Birkenhake, Ch.; Lange, H., Complex tori, (1999), Birkhäuser · Zbl 0945.14027 [6] Broustet, A., Constantes de Seshadri du diviseur anticanonique des surfaces de del Pezzo, Enseign. math. (2), 52, 3-4, 231-238, (2006) · Zbl 1112.14010 [7] J.W.S. Cassels, An introduction to the geometry of numbers, Berlin, 1997 · Zbl 0866.11041 [8] O. Debarre, Seshadri Constants of abelian varieties, in: A. Collino, A. Conte, M. Marchiso (Eds.), The Fano Conference, Proceedings, Torino 2002, Torino, 2004, pp. 379-394 · Zbl 1077.14011 [9] Demailly, J.-P., Singular Hermitian metrics on positive line bundles, (), 87-104 · Zbl 0784.32024 [10] Fuentes García, L., Seshadri constants on ruled surfaces: the rational and the elliptic cases, Manuscripta math., 119, 4, 483-505, (2006) · Zbl 1097.14006 [11] P. Gruber, C. Lekkerkerker, Geometry of numbers, Amsterdam, 1987 · Zbl 0611.10017 [12] Hayashida, T.; Nishi, M., Existence of curves of genus two on a product of two elliptic curves, J. math. soc. Japan, 17, 1, 1-16, (1965) · Zbl 0132.41701 [13] Kong, J., Seshadri constants on Jacobian of curves, Trans. amer. math. soc., 355, 8, 3175-3180, (2003) · Zbl 1016.14014 [14] Knutsen, A.L., A note on Seshadri constants on general K3 surfaces · Zbl 1171.14023 [15] Lange, H.; Birkenhake, Ch., Complex abelian varieties, Grundlehren math. wiss., vol. 302, (1992), Springer-Verlag · Zbl 0779.14012 [16] Lazarsfeld, R., Lengths of periods and Seshadri constants of abelian varieties, Math. res. lett., 3, 439-447, (1997) · Zbl 0890.14025 [17] Lazarsfeld, R., Positivity in algebraic geometry I, (2004), Springer-Verlag [18] Nakamaye, M., Seshadri constants on abelian varieties, Amer. J. math., 118, 621-635, (1996) · Zbl 0893.14014 [19] Ross, J., Seshadri constants on symmetric products of curves, Math. res. lett., 14, 1, 63-75, (2007) · Zbl 1124.14012 [20] T. Szemberg, Global and local positivity of line bundles, Habilitationsschrift, Essen, 2001 · Zbl 0977.14003 [21] Tutaj-Gasinska, H., A bound for Seshadri constants on $$\mathbb{P}^2$$, Math. nachr., 257, 108-116, (2003) · Zbl 1110.14303 [22] Tutaj-Gasinska, H., Seshadri constants in half-periods of an abelian surface, J. pure appl. algebra, 194, 1-2, 183-191, (2004) · Zbl 1060.14009
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.