A simple combinatorial criterion for projective toric manifolds with dual defect
We show that any smooth lattice polytope P with codegree greater or equal than (dim(P) + 3)/2 (or equivalently, with degree smaller than dim(P)/2), defines a dual defective projective toric manifold. This implies that P is ℚ-normal (in the terminology of [11]) and answers partially an adjunction-the...
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2010
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10732780_v17_n3_p435_Dickenstein http://hdl.handle.net/20.500.12110/paper_10732780_v17_n3_p435_Dickenstein |
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| Sumario: | We show that any smooth lattice polytope P with codegree greater or equal than (dim(P) + 3)/2 (or equivalently, with degree smaller than dim(P)/2), defines a dual defective projective toric manifold. This implies that P is ℚ-normal (in the terminology of [11]) and answers partially an adjunction-theoretic conjecture by Beltrametti- Sommese (see [5], [4], [11]). Also, it follows from [24] that smooth lattice polytopes with this property are precisely strict Cayley polytopes, which completes the answer in [11] of a question in [1] for smooth polytopes. © International Press 2010. |
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