Varieties of apolar subschemes of toric surfaces
Abstract
Powersum varieties, also called varieties of sums of powers, have provided examples of interesting relations between varieties since their first appearance in the 19th century. One of the most useful tools to study them is apolarity, a notion originally related to the action of differential operators on the polynomial ring. In this work we make explicit how one can see apolarity in terms of the Cox ring of a variety. In this way powersum varieties are a special case of varieties of apolar schemes; we explicitely describe examples of such varieties in the case of two toric surfaces, when the Cox ring is particularly wellbehaved.
 Publication:

arXiv eprints
 Pub Date:
 January 2016
 arXiv:
 arXiv:1601.00694
 Bibcode:
 2016arXiv160100694G
 Keywords:

 Mathematics  Algebraic Geometry;
 14C99;
 14M99
 EPrint:
 25 pages, to appear in Arkiv f\"or Matematik