Title: Flat families of point schemes for connected graded algebras,
Abstract: We study truncated point schemes of connected graded algebras as families
over the parameter space of varying relations for the algebras, proving that
the families are flat over the open dense locus where the point schemes achieve
the expected (i.e. minimal) dimension.
When the truncated point scheme is zero-dimensional we obtain its number of
points counted with multiplicity via a Chow ring computation. This latter
application in particular confirms a conjecture of Brazfield to the effect that
a generic two-generator, two-relator 4-dimensional Artin-Schelter regular
algebra has seventeen truncated point modules of length six.