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Maps of Mori Dream Spaces in Cox coordinates Part I: existence of descriptions

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  • J. BuczyÅ„ski
  • O. KÄ™dzierski

Abstract

Any rational map between affine spaces, projective spaces or toric varieties can be described in terms of their affine, homogeneous, or Cox coordinates. We show an analogous statement in the setting of Mori Dream Spaces. More precisely (in the case of regular maps) we show that there exists a finite extension of the Cox ring of the source, such that the regular map lifts to a morphism from the Cox ring of the target to the finite extension. Moreover the extension only involves roots of homogeneous elements. Such a description of the map can be applied in practical computations.

Suggested Citation

  • J. BuczyÅ„ski & O. KÄ™dzierski, 2018. "Maps of Mori Dream Spaces in Cox coordinates Part I: existence of descriptions," Mathematische Nachrichten, Wiley Blackwell, vol. 291(4), pages 576-592, March.
    • Handle: RePEc:bla:mathna:v:291:y:2018:i:4:p:576-592
    DOI: 10.1002/mana.201600287
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