2 citations · 5 across the 4 of their papers we have counts for
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Geometric Divisors in Normal Local Domains
John Brevik, Scott Nollet
Let A be the local ring at a point of a normal complex variety with completion R. Srinivas has asked about the possible images of the induced map from Cl A to Cl R over all geometr…
Grothendieck-Lefschetz Theorem with Base Locus
John Brevik, Scott Nollet
We compute the divisor class group of the general hypersurface Y of a complex projective normal variety X of dimension at least four containing a fixed base locus Z. We deduce that…
Srinivas' Problem for Rational Double Points
John Brevik, Scott Nollet
For the completion B of a local geometric normal domain, V. Srinivas asked which subgroups of Cl B arise as the image of the map from Cl A to Cl B on class groups as A varies among…
Picard Groups of Normal Surfaces
John Brevik, Scott Nollet
We study the fixed singularities imposed on members of a linear system of surfaces in P^3_C by its base locus Z. For a 1-dimensional subscheme Z \subset P^3 with finitely many poin…
Local Picard Groups
John Brevik, Scott Nollet
We use our extension of the Noether-Lefschetz theorem to describe generators of the class groups at the local rings of singularities of very general hypersurfaces containing a fixe…
Noether-Lefschetz theorem with base locus
John Brevik, Scott Nollet
We compute the class groups of very general normal surfaces in complex projective three-space containing an arbitrary base locus , thereby extending the classic Noether-Lefschet…