The Cox Ring of an Algebraic Variety with Torus Action
نویسنده
چکیده
We investigate the Cox ring of a normal complete variety X with algebraic torus action. A first result relates the Cox ring of X to that of a maximal geometric quotient of X. As a consequence, we obtain a complete description of the Cox ring in terms of generators and relations for varieties with torus action of complexity one. Applied to smooth K-surfaces, this gives a description of the Cox ring in terms of Orlik-Wagreich graphs. The latter allows, for example, to determine Cox rings of singular del Pezzo surfaces with K -action via their resolution graphs.
منابع مشابه
The Cox Ring of an Algebraic Variety with Torus Action
We investigate the Cox ring of a normal complete variety X with algebraic torus action. Our first results relate the Cox ring of X to that of a maximal geometric quotient of X . As a consequence, we obtain a complete description of the Cox ring in terms of generators and relations for varieties with torus action of complexity one. Moreover, we provide a combinatorial approach to the Cox ring us...
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We investigate the Cox ring of a normal complete variety X with algebraic torus action. Our first results relate the Cox ring of X to that of a maximal geometric quotient of X. As a consequence, we obtain a complete description of the Cox ring in terms of generators and relations for varieties with torus action of complexity one. Moreover, we provide a combinatorial approach to the Cox ring usi...
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