Genus zero Gopakumar–Vafa type invariants for Calabi–Yau 4-folds II: Fano 3-folds
نویسندگان
چکیده
منابع مشابه
Deformations of Q-calabi-yau 3-folds and Q-fano 3-folds of Fano Index 1
In this article, we prove that any Q-Calabi-Yau 3-fold with only ordinary terminal singularities and any Q-Fano 3-fold of Fano index 1 with only terminal singularities have Q-smoothings.
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This paper classifies all toric Fano 3-folds with terminal singularities. This is achieved by solving the equivalent combinatoric problem; that of finding, up to the action of GL(3, Z), all convex polytopes in Z which contain the origin as the only non-vertex lattice point. 0. Background and Introduction A toric variety of dimension n over an algebraically closed field k is a normal variety X t...
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We shall give the best possible upper bound of the Fano indices together with a characterization of those Q-Fano 3-folds which attain the maximum in terms of graded rings. 0. Introduction Q-Fano 3-folds play important roles in birational algebraic geometry. They have been studied by several authors since G. Fano. In this paper, we study Q-Fano 3-folds from the view of their Fano indices (See de...
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Theorem 1 Suppose X is a smooth toric Fano 4-fold. Then X admits a totally nondegenerate abelian surface if X = P4, if X = P1 × P3 (type B4), or if X is a product of two smooth toric Del Pezzo surfaces (i.e. of type C4, D13, H8, L7, L8, L9, Q10, Q11, K4, U5, S2 × S2, S2 × S3 or S3 × S3). Otherwise there is no such embedding, unless possibly X is of type C3, D7, D10, D11, D14, D17, D18, G3, G4, ...
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In this article, we prove that any Q-factorial weak Fano 3-fold with only terminal singularities has a smoothing. 0. Introduction Definition 0.1. Let X be a normal Gorenstein projective variety of dimension 3 over C which has only terminal singularities. (1) If −KX is ample, we call X a Fano 3-fold. (2) If −KX is nef and big, we call X a weak Fano 3-fold. Definition 0.2. Let X be a normal Goren...
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ژورنال
عنوان ژورنال: Communications in Contemporary Mathematics
سال: 2019
ISSN: 0219-1997,1793-6683
DOI: 10.1142/s0219199719500603