Jarek Buczynski, Texas A&M University

Maps of toric varieties in homogeneous coordinates

The Cox ring provides a coordinate system on a toric variety analogous to the homogeneous coordinate ring of projective space. This allows to relatively easily construct and describe subvarieties in toric varieties by giving equations (analogously to homogeneous equations in projective space), or to describe sheaves by giving graded modules. Rational maps between projective spaces are described using polynomials in the coordinate ring. In our work we generalise the description of maps to toric varieties and we provide a unified description of maps between toric varieties in terms of their homogeneous coordinates. The maps in consideration do not necessarily preserve the toric structure. Introducing roots of polynomials is necessary even in the simplest examples. (Joint work with Gavin Brown.)

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