Ideals with a radical generic initial ideal

Abstract: The choice of a term order allows us to associate to any ideal I a monomial ideal, called the initial ideal of I. The initial ideal of I depends not only on the choice of a term order, but also on the system of coordinates. Nevertheless, many properties of I can be inferred from those of its initial ideal(s). For a given term order and in a generic coordinate system, however, the initial ideal of I is always the same and it is then called the generic initial ideal of I. In my talk, I will introduce a family of ideals whose generic initial ideal is independent of the choice of both the term order and of the system of coordinates. These are exactly the multigraded homogeneous ideals which have a radical generic initial ideal. Multigraded ideals which have a radical generic initial ideal show interesting rigidity properties, which e.g. allow us to deduce information on their universal Groebner bases. In the talk, I will present examples of ideals which belong to this class and of what we can deduce about them using this machinery. The original work in the talk is joint with Aldo Conca and Emanuela De Negri.

commutative algebra

Audience: researchers in the topic

Fellowship of the Ring

Series comments: Description: National Commutative Algebra Seminar

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