The number of vertices of a Fano polytope

Cinzia Casagrande[1]

  • [1] Università di Pisa Dipartimento di Matematica “L. Tonelli” Largo Bruno Pontecorvo, 5 56127 Pisa (Italy)

Annales de l’institut Fourier (2006)

  • Volume: 56, Issue: 1, page 121-130
  • ISSN: 0373-0956

Abstract

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Let X be a Gorenstein, ℚ -factorial, toric Fano variety. We prove two conjectures on the maximal Picard number of X in terms of its dimension and its pseudo-index, and characterize the boundary cases. Equivalently, we determine the maximal number of vertices of a simplicial reflexive polytope.

How to cite

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Casagrande, Cinzia. "The number of vertices of a Fano polytope." Annales de l’institut Fourier 56.1 (2006): 121-130. <http://eudml.org/doc/10136>.

@article{Casagrande2006,
abstract = {Let $X$ be a Gorenstein, $\mathbb\{Q\}$-factorial, toric Fano variety. We prove two conjectures on the maximal Picard number of $X$ in terms of its dimension and its pseudo-index, and characterize the boundary cases. Equivalently, we determine the maximal number of vertices of a simplicial reflexive polytope.},
affiliation = {Università di Pisa Dipartimento di Matematica “L. Tonelli” Largo Bruno Pontecorvo, 5 56127 Pisa (Italy)},
author = {Casagrande, Cinzia},
journal = {Annales de l’institut Fourier},
keywords = {toric varieties; Fano varieties; reflexive polytopes; Fano polytopes; toric variety; Fano variety; reflexive polytope; Fano polytope},
language = {eng},
number = {1},
pages = {121-130},
publisher = {Association des Annales de l’institut Fourier},
title = {The number of vertices of a Fano polytope},
url = {http://eudml.org/doc/10136},
volume = {56},
year = {2006},
}

TY - JOUR
AU - Casagrande, Cinzia
TI - The number of vertices of a Fano polytope
JO - Annales de l’institut Fourier
PY - 2006
PB - Association des Annales de l’institut Fourier
VL - 56
IS - 1
SP - 121
EP - 130
AB - Let $X$ be a Gorenstein, $\mathbb{Q}$-factorial, toric Fano variety. We prove two conjectures on the maximal Picard number of $X$ in terms of its dimension and its pseudo-index, and characterize the boundary cases. Equivalently, we determine the maximal number of vertices of a simplicial reflexive polytope.
LA - eng
KW - toric varieties; Fano varieties; reflexive polytopes; Fano polytopes; toric variety; Fano variety; reflexive polytope; Fano polytope
UR - http://eudml.org/doc/10136
ER -

References

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