INVESTIGADORES
DICKENSTEIN Alicia Marcela
congresos y reuniones científicas
Título:
The structure of smooth lattice polytopes with high codegree
Autor/es:
A. DICKENSTEIN
Lugar:
Rio de Janeiro, Brasil
Reunión:
Congreso; ALGA 2010; 2010
Institución organizadora:
IMPA
Resumen:
<!-- /* Style Definitions */ p.MsoNormal, li.MsoNormal, div.MsoNormal {mso-style-parent:""; margin:0cm; margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:12.0pt; font-family:"Times New Roman"; mso-fareast-font-family:"Times New Roman";} @page Section1 {size:612.0pt 792.0pt; margin:70.85pt 3.0cm 70.85pt 3.0cm; mso-header-margin:36.0pt; mso-footer-margin:36.0pt; mso-paper-source:0;} div.Section1 {page:Section1;} --> A lattice polytope P in R^n is the convex hull of a finite set of integer points. The codegree c of P is the smallest positive integer c such that the dilated polytope cP has an interior integer point. We say that P has high codegree if c > n/2 + 1. Following joint work with Sandra di Rocco, Benjamin Nill and Ragni Piene, we show the Cayley structure of smooth lattice polytopes with high codegree using tools from projective algebraic geometry and from combinatorics. This answers for smooth toric varieties a question by Batyrev and Nill and solves partially an adjunction-theoretic conjecture by Beltrametti-Sommese.
