On projective toric varieties whose defining ideals have minimal generators of the highest degree

Ogata, Shoetsu

doi:10.5802/aif.2005

On projective toric varieties whose defining ideals have minimal generators of the highest degree
[Sur les variétés toriques projectives dont les idéaux annulateurs ont des générateurs minimaux de plus haut degré]

Ogata, Shoetsu ¹

¹ Tohoku University, Mathematical Institute, Sendai 980 (Japon)

Annales de l'Institut Fourier, Tome 53 (2003) no. 7, pp. 2243-2255.

Résumé
Abstract

Il est connu que les générateurs de l’idéal annulateur d’une variété torique projective de dimension $n$ , plongée par les sections globales d’un fibré en droites normalement engendré, sont de degré au plus $n + 1$ . Nous caractérisons les variétés projectives de dimension $n$ dont un générateur au moins de l’idéal annulateur doit être de degré $n + 1$ .

It is known that generators of ideals defining projective toric varieties of dimension $n$ embedded by global sections of normally generated line bundles have degree at most $n + 1$ . We characterize projective toric varieties of dimension $n$ whose defining ideals must have elements of degree $n + 1$ as generators.

MR Zbl

DOI : 10.5802/aif.2005

Classification : 14M25, 14J40, 52B20
Keywords: toric varieties, convex polytopes, generators of ideals
Mot clés : variétés toriques, polytopes convexes, générateurs d'idéaux

Affiliations des auteurs :

Ogata, Shoetsu ¹

¹ Tohoku University, Mathematical Institute, Sendai 980 (Japon)

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     title = {On projective toric varieties whose defining ideals have minimal generators of the highest degree},
     journal = {Annales de l'Institut Fourier},
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     volume = {53},
     number = {7},
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Ogata, Shoetsu. On projective toric varieties whose defining ideals have minimal generators of the highest degree. Annales de l'Institut Fourier, Tome 53 (2003) no. 7, pp. 2243-2255. doi : 10.5802/aif.2005. http://www.numdam.org/articles/10.5802/aif.2005/

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