13 citations · 39 across the 13 of their papers we have counts for
13 papers · 1 filter
Smoothing surfaces on fourfolds
Scott Nollet, A. P. Rao
If are vector bundles of ranks on a smooth fourfold and is globally generated, it is well known that the…
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…
Detaching embedded points
Dawei Chen, Scott Nollet
We show that if is obtained from a codimension two local complete intersection by adding embedded points of multiplicity , then is a flat li…
Hilbert scheme of a pair of codimension two linear subspaces
Dawei Chen, Izzet Coskun, Scott Nollet
We study the component H_n of the Hilbert scheme whose general point parameterizes a pair of codimension two linear subspaces in P^n for n > 2. We show that H_n is smooth and isomo…
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…
Birationality of étale morphisms via surgery
Scott Nollet, Laurence R. Taylor, Frederico Xavier
We use a counting argument and surgery theory to show that if is a sufficiently general algebraic hypersurface in , then any local diffeomorphism o…
Holomorphic injectivity and the Hopf map
Scott Nollet, Frederico Xavier
We give sharp conditions on a local biholomorphism which ensure global injectivity. For , such a map is injective if for each complex line $l \sub…
Curves on a Double Surface
Scott Nollet, Enrico Schlesinger
Let F be a smooth surface in a smooth projective threefold T, and let X=2F be the first infinitesimal neighborhood of X in T. A locally Cohen-Macaulay curve C in X gives rise to tw…
Hilbert Schemes of Degree Four Curves
Scott Nollet, Enrico Schlesinger
In this paper we determine the irreducible components of the Hilbert schemes H(4,g) of locally Cohen-Macaulay space curves of degree four and arbitrary arithmetic genus g. We show…