The Michigan Mathematical Journal

Projective manifolds containing a large linear subspace with nef normal bundle

Carla Novelli and Gianluca Occhetta

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Michigan Math. J., Volume 60, Issue 2 (2011), 441-462.

First available in Project Euclid: 14 July 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14E30: Minimal model program (Mori theory, extremal rays)
Secondary: 14S40 14S65 14M15: Grassmannians, Schubert varieties, flag manifolds [See also 32M10, 51M35]


Novelli, Carla; Occhetta, Gianluca. Projective manifolds containing a large linear subspace with nef normal bundle. Michigan Math. J. 60 (2011), no. 2, 441--462. doi:10.1307/mmj/1310667984.

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  • M. Andreatta, E. Ballico, and J. A. Wiśniewski, Projective manifolds containing large linear subspaces, Classification of irregular varieties (Trento, 1990), Lecture Notes in Math., 1515, pp. 1–11, Springer-Verlag, Berlin, 1992.
  • M. Andreatta and J. A. Wiśniewski, A note on nonvanishing and applications, Duke Math. J. 72 (1993), 739–755.
  • –––, On manifolds whose tangent bundle contains an ample subbundle, Invent. Math. 146 (2001), 209–217.
  • E. Ballico, Uniform vector bundles of rank $(n+1)$ on $\bold P_n,$ Tsukuba J. Math. 7 (1983), 215–226.
  • E. Ballico and J. A. Wiśniewski, On Bănică sheaves and Fano manifolds, Compositio Math. 102 (1996), 313–335.
  • M. C. Beltrametti and P. Ionescu, On manifolds swept out by high dimensional quadrics, Math. Z. 260 (2008), 229–236.
  • M. C. Beltrametti and A. J. Sommese, The adjunction theory of complex projective varieties, de Gruyter Exp. Math., 16, de Gruyter, Berlin, 1995.
  • M. C. Beltrametti, A. J. Sommese, and J. A. Wiśniewski, Results on varieties with many lines and their applications to adjunction theory, Complex algebraic varieties (Bayreuth, 1990), Lecture Notes in Math., 1507, pp. 16–38, Springer-Verlag, Berlin, 1992.
  • L. Bonavero, C. Casagrande, and S. Druel, On covering and quasi-unsplit families of curves, J. Eur. Math. Soc. 9 (2007), 45–57.
  • F. Campana, Coréduction algébrique d'un espace analytique faiblement kählérien compact, Invent. Math. 63 (1981), 187–223.
  • E. Chierici and G. Occhetta, The cone of curves of Fano varieties of coindex four, Internat. J. Math. 17 (2006), 1195–1221.
  • M. Cornalba, Una osservazione sulla topologia dei rivestimenti ciclici di varietà algebriche, Boll. Un. Mat. Ital. A (5) 18 (1981), 323–328.
  • O. Debarre, Higher-dimensional algebraic geometry, Springer-Verlag, New York, 2001.
  • L. Ein, Varieties with small dual varieties. II, Duke Math. J. 52 (1985), 895–907.
  • G. Elencwajg, A. Hirschowitz, and M. Schneider, Les fibres uniformes de rang au plus $n$ sur $\bold P_n(\bold C)$ sont ceux qu'on croit, Vector bundles and differential equations (Nice, 1979), Progr. Math., 7, pp. 37–63, Birkhäuser, Boston, 1980.
  • P. Ellia, Sur les fibrés uniformes de rang $(n+1)$ sur $\bold P^n,$ Mém. Soc. Math. France (N.S.) 7 (1982).
  • B. Fu, Inductive characterization of hyperquadrics, Math. Ann. 340 (2008), 185–194.
  • T. Fujita, Impossibility criterion of being an ample divisor, J. Math. Soc. Japan 34 (1982), 355–363.
  • –––, On polarized manifolds whose adjoint bundles are not semipositive, Algebraic geometry (Sendai, 1985), Adv. Stud. Pure Math., 10, pp. 167–178, North-Holland, Amsterdam, 1987.
  • P. Ionescu, Generalized adjunction and applications, Math. Proc. Cambridge Philos. Soc. 99 (1986), 457–472.
  • S. Kebekus and S. J. Kovács, Are rational curves determined by tangent vectors? Ann. Inst. Fourier (Grenoble) 54 (2004), 53–79.
  • S. Kobayashi and T. Ochiai, Characterizations of complex projective spaces and hyperquadrics, J. Math. Kyoto Univ. 13 (1973), 31–47.
  • J. Kollár, Rational curves on algebraic varieties, Ergeb. Math. Grenzgeb. (3), 32, Springer-Verlag, Berlin, 1996.
  • C. Novelli and G. Occhetta, Manifolds covered by lines and extremal rays, Canad. Math. Bull. (to appear).
  • G. Occhetta and D. Panizzolo, Fano–Mori elementary contractions with reducible general fiber, Kodai Math. J. 28 (2005), 559–576.
  • V. Paterno, Scoppiamenti di Grassmanniane e varietà di Fano, Graduate thesis, Università di Trento, 2006.
  • M. Reid, The intersection of two quadrics, Ph.D. thesis, Cambridge University, 1972, $\langle$$\rangle.$
  • E. Sato, Projective manifolds swept out by large-dimensional linear spaces, Tôhoku Math. J. (2) 49 (1997), 299–321.
  • J. A. Wiśniewski, On a conjecture of Mukai, Manuscripta Math. 68 (1990), 135–141.
  • –––, On contractions of extremal rays of Fano manifolds, J. Reine Angew. Math. 417 (1991), 141–157.
  • –––, On deformation of nef values, Duke Math. J. 64 (1991), 325–332.
  • F. L. Zak, Tangents and secants of algebraic varieties, Transl. Math. Monogr., 127, Amer. Math. Soc., Providence, RI, 1993.