2016/01/04 by Matteo Gallet, Kristian Ranestad, Gallet, Matteo +3
Mathematics · #14C99 #14M99 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14C99 #msc:14M99
paper · pdf · doi:10.48550/arxiv.1601.00694
25 pages, to appear in Arkiv för Matematik
arxiv created 2017/06/05 · arxiv updated 2017/06/07
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 well-behaved.