Abstract:
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.
Registro:
Documento: |
Artículo
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Título: | A simple combinatorial criterion for projective toric manifolds with dual defect |
Autor: | Dickenstein, A.; Nill, B. |
Filiación: | Departamento de Matemática, FCEN, Universidad de Buenos Aires, C1428EGA Buenos Aires, Argentina Department of Mathematics, University of Georgia, Athens, GA 30602, United States
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Año: | 2010
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Volumen: | 17
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Número: | 3
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Página de inicio: | 435
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Página de fin: | 448
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DOI: |
http://dx.doi.org/10.4310/MRL.2010.v17.n3.a5 |
Título revista: | Mathematical Research Letters
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Título revista abreviado: | Math. Res. Lett.
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ISSN: | 10732780
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10732780_v17_n3_p435_Dickenstein |
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Citas:
---------- APA ----------
Dickenstein, A. & Nill, B.
(2010)
. A simple combinatorial criterion for projective toric manifolds with dual defect. Mathematical Research Letters, 17(3), 435-448.
http://dx.doi.org/10.4310/MRL.2010.v17.n3.a5---------- CHICAGO ----------
Dickenstein, A., Nill, B.
"A simple combinatorial criterion for projective toric manifolds with dual defect"
. Mathematical Research Letters 17, no. 3
(2010) : 435-448.
http://dx.doi.org/10.4310/MRL.2010.v17.n3.a5---------- MLA ----------
Dickenstein, A., Nill, B.
"A simple combinatorial criterion for projective toric manifolds with dual defect"
. Mathematical Research Letters, vol. 17, no. 3, 2010, pp. 435-448.
http://dx.doi.org/10.4310/MRL.2010.v17.n3.a5---------- VANCOUVER ----------
Dickenstein, A., Nill, B. A simple combinatorial criterion for projective toric manifolds with dual defect. Math. Res. Lett. 2010;17(3):435-448.
http://dx.doi.org/10.4310/MRL.2010.v17.n3.a5