Remarks on defective Fano manifolds

被引：0

作者：

Ionescu P. ^{[1
]}

Russo F. ^{[2
]}

机构：

[1] Dipartimento di Matematica e Informatica, Università degli Studi di Ferrara, Via Machiavelli, 30, Ferrara

[2] Dipartimento di Matematica e Informatica, Università degli Studi di Catania, Viale A. Doria, 6, Catania

来源：

ANNALI DELL'UNIVERSITA' DI FERRARA | 2017年 / 63卷 / 1期

关键词：

Conic connected; Dual defective; Fano manifold; Local quadratic entry locus;

D O I：

10.1007/s11565-017-0270-6

中图分类号：

学科分类号：

摘要：

This note continues our previous work on special secant defective (specifically, conic connected and local quadratic entry locus) and dual defective manifolds. These are now well understood, except for the prime Fano ones. Here we add a few remarks on this case, completing the results in our papers (Russo in Math Ann 344:597–617, 2009; Ionescu and Russo in Compos Math 144:949–962, 2008; Ionescu and Russo in J Reine Angew Math 644:145–157, 2010; Ionescu and Russo in Am J Math 135:349–360, 2013; Ionescu and Russo in Math Res Lett 21:1137–1154, 2014); see also the recent book (Russo, On the Geometry of Some Special Projective Varieties, Lecture Notes of the Unione Matematica Italiana, Springer, 2016). © 2017, Università degli Studi di Ferrara.

引用

页码：133 / 146

页数：13

共 27 条

[1]

Ballico E., Chiantini L., On smooth subcanonical varieties of codimension 2 in P<sup>n</sup>, n≥ 4, Ann. Math. Pura Appl, 135, pp. 99-117, (1983)

[2]

Barth W., Larsen M.E., On the homotopy groups of complex projective algebraic manifolds, Math. Scand, 30, pp. 88-94, (1972)

[3]

Beltrametti M.C., Fania M.L., Sommese A.J., On the discriminant variety of a projective manifold, Forum Math, 4, pp. 529-547, (1992)

[4]

Bonavero L., Horing A., Counting conics in complete intersections, Acta Math. Vietnam, 35, pp. 23-30, (2010)

[5]

Ein L., Varieties with small dual variety. I, Invent. Math, 86, pp. 63-74, (1986)

[6]

Ein L., Varieties with small dual variety. II, Duke Math. J, 52, pp. 895-907, (1985)

[7]

Fu B., Inductive characterizations of hyperquadrics, Math. Ann, 340, pp. 185-194, (2008)

[8]

Fujita T., Classification Theories of Polarized Varieties, London Mathematical Society Lecture Note Series, vol. 155, Cambridge University Press, (1990)

[9]

Hwang J.M., Geometry of minimal rational curves on Fano manifolds, School on Vanishing Theorems and Effective Results in Algebraic Geometry (Trieste, 2000), ICTP Lecture Notes, vol. 6. Abdus Salam Int. Cent. Theoret. Phys, pp. 335-393, (2001)

[10]

Hwang J.M., Kebekus S., Geometry of chains of minimal rational curves, J. Reine Angew. Math, 584, pp. 173-194, (2005)

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