A+ CATEGORY SCIENTIFIC UNIT

Maps of toric varieties in Cox coordinates

Volume 222 / 2013

Gavin Brown, Jarosław Buczyński Fundamenta Mathematicae 222 (2013), 213-267 MSC: Primary 14M25; Secondary 14E05, 14Q99. DOI: 10.4064/fm222-3-2

Abstract

The Cox ring provides a coordinate system on a toric variety analogous to the homogeneous coordinate ring of projective space. Rational maps between projective spaces are described using polynomials in the coordinate ring, and we generalise this to toric varieties, providing a unified description of arbitrary rational maps between toric varieties in terms of their Cox coordinates. Introducing formal roots of polynomials is necessary even in the simplest examples.

Authors

  • Gavin BrownSchool of Mathematics
    Loughborough University
    LE11 3TU, United Kingdom
    e-mail
  • Jarosław BuczyńskiInstitute of Mathematics
    Polish Academy of Sciences
    P.O. Box 21
    Śniadeckich 8
    00-956 Warszawa, Poland
    e-mail

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