Artículo
Dickenstein, A.; Di Rocco, S.; Piene, R. "Classifying smooth lattice polytopes via toric fibrations" (2009) Advances in Mathematics. 222(1):240-254
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Abstract:
We show that any smooth Q-normal lattice polytope P of dimension n and degree d is a strict Cayley polytope if n ≥ 2 d + 1. This gives a sharp answer, for this class of polytopes, to a question raised by V.V. Batyrev and B. Nill. © 2009 Elsevier Inc. All rights reserved.
Registro:
| Documento: | Artículo |
| Título: | Classifying smooth lattice polytopes via toric fibrations |
| Autor: | Dickenstein, A.; Di Rocco, S.; Piene, R. |
| Filiación: | Departamento de Matemática, FCEN, Universidad de Buenos Aires, Ciudad Universitaria - Pab. I, 1428 Buenos Aires, Argentina Department of Mathematics, KTH, SE-10044 Stockholm, Sweden CMA/Department of Mathematics, University of Oslo, PO Box 1053 Blindern, NO-0316 Oslo, Norway |
| Palabras clave: | Cayley polytope; Lattice polytope; Nef value; Toric fibration; Toric variety |
| Año: | 2009 |
| Volumen: | 222 |
| Número: | 1 |
| Página de inicio: | 240 |
| Página de fin: | 254 |
| DOI: | http://dx.doi.org/10.1016/j.aim.2009.04.002 |
| Título revista: | Advances in Mathematics |
| Título revista abreviado: | Adv. Math. |
| ISSN: | 00018708 |
| PDF: | https://bibliotecadigital.exactas.uba.ar/download/paper/paper_00018708_v222_n1_p240_Dickenstein.pdf |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00018708_v222_n1_p240_Dickenstein |
Referencias:
- Batyrev, V.V., Nill, B., Multiples of lattice polytopes without interior lattice points (2007) Mosc. Math. J., 7 (2), pp. 195-207
- Beltrametti, M.C., Sommese, A.J., On the adjunction theoretic classification of polarized varieties (1992) J. Reine Angew. Math., 427, pp. 157-192
- Beltrametti, M.C., Sommese, A.J., The Adjunction Theory of Complex Projective Varieties (1995) de Gruyter Exp. Math., 16. , Walter de Gruyter & Co., Berlin
- Beltrametti, M.C., Sommese, A.J., Wiśniewski, J.A., Results on varieties with many lines and their applications to adjunction theory (1992) Lecture Notes in Math., 1507, pp. 16-38. , Complex Algebraic Varieties. Bayreuth, 1990, Springer-Verlag, Berlin
- Casagrande, C., Di Rocco, S., Projective Q-factorial toric varieties covered by lines (2008) Commun. Contemp. Math., 10 (3), pp. 363-389
- Clemens, H., Kollàr, J., Mori, S., Higher-dimensional complex geometry (1988) Astérisque, 166
- Di Rocco, S., Projective duality of toric manifolds and defect polytopes (2006) Proc. London Math. Soc. (3), 93 (1), pp. 85-104
- Di Rocco, S., Sommese, A.J., Chern numbers of ample vector bundles on toric surfaces (2004) Trans. Amer. Math. Soc., 356 (2), pp. 587-598
- Haase, C., Nill, B., Payne, S., (2008) Cayley decompositions of lattice polytopes and upper bounds for h*-polynomials, , preprint. arXiv:0804.3667 J. Reine Angew. Math., in press
- Kawamata, Y., The cone of curves of algebraic varieties (1984) Ann. of Math. (2), 119 (3), pp. 603-633
- Lanteri, A., Struppa, D., Projective manifolds whose topology is strongly reflected in their hyperplane sections (1986) Geom. Dedicata, 21 (3), pp. 357-374
- Mustaţǎ, M., Vanishing theorems on toric varieties (2002) Tohoku Math. J. (2), 54 (3), pp. 451-470
- Oda, T., Convex Bodies and Algebraic Geometry (1988) Ergeb. Math. Grenzgeb. (3), 15. , Springer-Verlag, Berlin
- Reid, M., Decomposition of toric morphisms (1983) Progr. Math., 36, pp. 395-418. , Arithmetic and Geometry, vol. II, Birkhäuser Boston, Boston, MA
- Ziegler, G.M., Lectures on Polytopes (1995) Grad. Texts in Math., 152. , Springer-Verlag, New York
Citas:
---------- APA ----------
Dickenstein, A., Di Rocco, S. & Piene, R. (2009) . Classifying smooth lattice polytopes via toric fibrations. Advances in Mathematics, 222(1), 240-254.http://dx.doi.org/10.1016/j.aim.2009.04.002
---------- CHICAGO ----------
Dickenstein, A., Di Rocco, S., Piene, R. "Classifying smooth lattice polytopes via toric fibrations" . Advances in Mathematics 222, no. 1 (2009) : 240-254.http://dx.doi.org/10.1016/j.aim.2009.04.002
---------- MLA ----------
Dickenstein, A., Di Rocco, S., Piene, R. "Classifying smooth lattice polytopes via toric fibrations" . Advances in Mathematics, vol. 222, no. 1, 2009, pp. 240-254.http://dx.doi.org/10.1016/j.aim.2009.04.002
---------- VANCOUVER ----------
Dickenstein, A., Di Rocco, S., Piene, R. Classifying smooth lattice polytopes via toric fibrations. Adv. Math. 2009;222(1):240-254.http://dx.doi.org/10.1016/j.aim.2009.04.002
