2023/09/13 by Homs, Roser, Winz, Anna-Lena
#13D02 #14C05 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.2309.06871
In the local setting, Gröbner cells are affine spaces that parametrize ideals in k[ [x,y] ] that share the same leading term ideal with respect to a local term ordering. In particular, all ideals in a cell have the same Hilbert function, so they provide a cellular decomposition of the punctual Hilbert scheme compatible with its Hilbert function stratification. We exploit the parametrization given in \citeHW21 via Hilbert-Burch matrices to compute the Betti strata, with hands-on examples of deformations that preserve the Hilbert function, and revisit some classical results along the way. Moreover, we move towards an explicit parametrization of all local Gröbner cells.