13 citations · 39 across the 13 of their papers we have counts for
16 papers
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…
The Hilbert Schemes of Degree Three Curves are Connected
Scott Nollet
In this paper we show that the Hilbert scheme of locally Cohen-Macaulay curves in $\Pthree$ of degree three and genus is connected. In contrast to , which is i…
Integral Subschemes of Codimension Two
Scott Nollet
In this paper we study the problem of describing the integral subschemes within a fixed even linkage class of subschemes in $\Pn$ of codimension two. In the case that is no…
Even Linkage Classes
Scott R. Nollet
In this paper the author generalizes the $\E$ and -type resolutions used by Martin-Deschamps and Perrin to subschemes of pure codimension in projective space, and shows that th…