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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