Sesión Álgebra Computacional y Conmutativa

Diciembre 15, 12:00 ~ 12:20

Copolarity of monomial ideals

Eduardo Sáenz-de-Cabezón

Polarization is an operation that transforms monomial ideals into squarefree monomial ideals. It has been used to study the conectedness of the Hilbert scheme (Hartshorne 1966) or the Cohen-Macaulay property of monomial ideals (cf. Stanley 1983 and Miller 2009) among other aplications.

We study the opposite operation, namely depolarization, and give a method to obtain the set of monomial ideals that share the same depolarization i.e. the we obtain the sets of copolar ideals. In particular we focus on some properties that are shared by copolar ideals and on some that, interestengly enough, are not.

Autores: Patricia Pascual-Ortigosa / Eduardo Sáenz-de-Cabezón.