Geodesic
Maps of toric varieties in Cox coordinates
Gavin Brown 1   ; Jarosław Buczyński 2
1 School of Mathematics Loughborough University LE11 3TU, United Kingdom
2 Institute of Mathematics Polish Academy of Sciences P.O. Box 21 Śniadeckich 8 00-956 Warszawa, Poland
Fundamenta Mathematicae, Tome 222 (2013) no. 3, pp. 213-267 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/fm222-3-2
Keywords: cox ring provides coordinate system toric variety analogous homogeneous coordinate ring projective space rational maps between projective spaces described using polynomials coordinate ring generalise toric varieties providing unified description arbitrary rational maps between toric varieties terms their cox coordinates introducing formal roots polynomials necessary even simplest examples

Gavin Brown  1   ; Jarosław Buczyński  2

1 School of Mathematics Loughborough University LE11 3TU, United Kingdom
2 Institute of Mathematics Polish Academy of Sciences P.O. Box 21 Śniadeckich 8 00-956 Warszawa, Poland 
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Gavin Brown; Jarosław Buczyński. Maps of toric varieties in Cox coordinates. Fundamenta Mathematicae, Tome 222 (2013) no. 3, pp. 213-267. doi: 10.4064/fm222-3-2

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