NORMAL CYCLIC POLYTOPES AND CYCLIC POLYTOPES THAT ARE NOT VERY AMPLE

作者：Hibi Takayuki; Higashitani Akihiro^*; Katthaen Lukas; Okazaki Ryota

来源：Journal of the Australian Mathematical Society, 2014, 96(1): 61-77.

DOI：10.1017/S1446788713000529

• cyclic polytope
• normal polytope
• very ample polytope

Let d and n be positive integers such that n %26gt;= d + 1 and tau(1),...,tau(n) integers such that tau(1)%26lt;...%26lt;tau(n). Let C-d(tau(1),...,tau(n)) subset of R-d denote the cyclic polytope of dimension d with n vertices (tau(1),tau(2)(1)...,tau(d)(1)),...,(tau(n),tau(2)(n),...,tau(d)(n)). We are interested in finding the smallest integer gamma(d) such that if tau(i+1) - tau(i) %26gt;= gamma(d) for 1 %26lt;= i %26lt; n, then C-d(tau(1),...,tau(n)) is normal. One of the known results is gamma(d) %26lt;= d(d + 1). In the present paper a new inequality gamma(d) %26lt;= d(2) - 1 is proved. Moreover, it is shown that if d %26gt;= 4 with tau(3) - tau(2) = 1, then C-d(tau(1),...,tau(n)) is not very ample.

• 出版日期2014-2