2016/02/25 by Bruns, Winfried, Conca, Aldo · 2 citations
#13A30 #13C40 #13D02 #13F20 #13P10 #14M12 #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.1602.07996
The goal of this paper is to present examples of families of homogeneous ideals in the polynomial ring over a field that satisfy the following condition: every product of ideals of the family has a linear free resolution. As we will see, this condition is strongly correlated to good primary decompositions of the products and good homological and arithmetical properties of the associated multi-Rees algebras. The following families will be discussed in detail: polymatroidal ideals, ideals generated by linear forms and Borel fixed ideals of maximal minors. The main tools are Gröbner bases and Sagbi deformation.