Variétés complexes dont l'éclatée en un point est de Fano

Bonavero, Laurent; Campana, Frédéric; Wiśniewski, Jarosław A.

doi:10.1016/s1631-073x(02)02284-7

Cited by 31 publications

(52 citation statements)

References 10 publications

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“…For the normal bundle to match, it is the blowup of a quadric hypersurface. AsX is obtained by contracting E 1 ∪ E 2 from X , it is a quadric hypersurface in P n+1 , and X is the quotient ofX by an involution that acts fixed point free in codimension one as in case (2).…”

Section: A Gorenstein Log Del Pezzo Surface Of Degree 4;mentioning

confidence: 99%

Characterization of projective spaces by Seshadri constants

Liu¹,

Zhuang²

2017

Math. Z.

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Section: A Gorenstein Log Del Pezzo Surface Of Degree 4;mentioning

confidence: 99%

Characterization of projective spaces by Seshadri constants

Liu¹,

Zhuang²

2017

Math. Z.

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“…In this case the theorem is actually the main theorem of [BCW02], where Fano manifolds which are the blow-up at a point of a smooth variety are classified (those varieties correspond to cases a), b) with t = 0 and d) of the above theorem).…”

Section: Mukai Conjecture Restricted To a Raymentioning

confidence: 99%

A Conjecture of Mukai Relating Numerical Invariants of Fano Manifolds

Andreatta¹

2009

Milan J. Math.

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A complex manifold X of dimension n such that the anticanonical bundle −K X := det TX is ample is called a Fano manifold. Besides the dimension, other two integers play an essential role in the classification of these manifolds, namely the pseudoindex of X, i X , which is the minimal anticanonical degree of rational curves on X, and the Picard number ρ X , the dimension of N 1 (X), the vector space generated by irreducible complex curves modulo numerical equivalence . A (generalization of a) conjecture of Mukai says that ρ X (i X − 1) ≤ n. In this paper we present some partial steps towards the conjecture, we show how one can interpretate and possibly solve it with the use of families of rational curves on a uniruled variety, and more generally with the instruments of Mori theory. We consider also other related problems: the description of some Fano manifolds which are at the border of the Mukai relations and how the pseudoindex changes via (some) birational transformation.

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“…We denote by U 6 a double cover of P 1 × P 2 whose branch locus is a smooth divisor of type (2,4). Let π 1 and π 2 be the two projections onto P 1 and P 2 , and let A and B are the ample generator of Pic(P 1 ) and Pic(P 2 ) respectively.…”

Section: Umentioning

confidence: 99%