The poset of depolarizations of a square free monomial ideal

 

Ponente: Patricia Pascual Ortigosa

Lugar: Seminario Mirian Andrés (Edificio CCT)

Hora: lunes 24 de julio, 12:00

Resumen: Polarization is an operation that transforms a monomial ideal of a polynomial ring R into a squarefree monomial ideal in another polynomial ideal that shares several important features of the original ideal.  Polarization is used in a wide variety of applications in the theory of monomial ideals. The inverse operation, depolarization, has however been less studied. It can be used to study squarefree monomial ideals using general monomial ideals which is convenient in a variety of situations. Depolarization is not unique, and in this talk we study the set of all possible depolarizations of a given squarefree monomial ideal obtaining the equivalence classes of monomial ideals with the same polarization. For this, we define depolarization orders and depolarization posets and study the ideals in them.

Nota: la charla se trata de una prueba de tiempo de la conferencia del mismo título que la ponente impartirá en el 4º Congreso de Jóvenes Investigadores de la RSME que tendrá lugar en la Universitat de València del 4 al 8 de septiembre.