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Nordström Cederholm Ernst: Om nolldimensionella ideal och initialideal

Bachelor thesis presentation

Time: Thu 2022-08-25 12.30 - 13.30

Location: Albano, House 1, Room T

Doctoral student: Nordström Cederholm Ernst

Abstract:

It is shown that every zero-dimensional monomial ideal I is the initial ideal of I(Σ), where Σ is the set of multivariate degrees of the monomials outside I. Macaulay may have known this and possibly had a draft towards a proof that precede the concept of the Gr¨obner basis. Using modern terminology, a universal Gröbner basis to I(Σ) is provided. As a consequence, it is shown that the function that maps finite affine varieties V , to the set of multivariate degrees of the monomials outside the initial ideal of I(V ), stabilizes directly