TY - JOUR

T1 - Algorithmic local monomialization of a binomial

T2 - a comparison of different approaches

AU - Gaube, Sabrina Alexandra

AU - Schober, Bernd

PY - 2022/12/9

Y1 - 2022/12/9

N2 - We investigate different approaches to transform a given binomial into a monomial via blowing up appropriate centers. In particular, we develop explicit implementations in {\sc Singular}, which allow to make a comparison on the basis of numerous examples. We focus on a local variant, where centers are not required to be chosen globally. Moreover, we do not necessarily demand that centers are contained in the singular locus. Despite these restrictions, the techniques are connected to the computation of \( p \)-adic integral whose data is given by finitely many binomials.

AB - We investigate different approaches to transform a given binomial into a monomial via blowing up appropriate centers. In particular, we develop explicit implementations in {\sc Singular}, which allow to make a comparison on the basis of numerous examples. We focus on a local variant, where centers are not required to be chosen globally. Moreover, we do not necessarily demand that centers are contained in the singular locus. Despite these restrictions, the techniques are connected to the computation of \( p \)-adic integral whose data is given by finitely many binomials.

KW - math.AG

KW - math.AC

KW - 13F65, 14B05, 14J17, 13P99

U2 - 10.48550/arXiv.2012.14910

DO - 10.48550/arXiv.2012.14910

M3 - Article

VL - 33

SP - 161

EP - 195

JO - International Journal of Algebra and Computation

JF - International Journal of Algebra and Computation

SN - 0218-1967

IS - 1

ER -