The End Curve Theorem for normal complex surface singularities (2008)
Neumann, Walter D, Wahl, Jonathan
We prove the ``End Curve Theorem,'' which states that a normal surface singularity $(X,o)$ with rational homology sphere link $\Sigma$ is a splice-quotient singularity if and only if it has an end...
Rational blowdowns and smoothings of surface singularities (2008)
Stipsicz, András I., Szabó, Zoltán, Wahl, Jonathan
In this paper, we give a necessary combinatorial condition for a negative-definite plumbing tree to be suitable for rational blowdown, or to be the graph of a complex surface singularity which admits...
Rational blow-downs and smoothings of surface singularities (2006)
Stipsicz, Andras I., Szabo, Zoltan, Wahl, Jonathan
In this paper we give a necessary combinatorial condition for a negative--definite plumbing tree to be suitable for rational blow--down, or to be the graph of a complex surface singularity which...
Topology, geometry, and equations of normal surface singularities (2005)
This expository talk is an expanded version of a lecture at G.-M. Greuel's 60th Birthday Conference in Kaiserslautern in October, 2004. We survey recent work of Neumann-Wahl and others on the...
Complete intersection singularities of splice type as universal abelian covers (2004)
Neumann, Walter D, Wahl, Jonathan
It has long been known that every quasi-homogeneous normal complex surface singularity with Q-homology sphere link has universal abelian cover a Brieskorn complete intersection singularity. We...
Complex surface singularities with integral homology sphere links (2003)
Neumann, Walter D., Wahl, Jonathan
While the topological types of {normal} surface singularities with homology sphere link have been classified, forming a rich class, until recently little was known about the possible analytic...
Universal abelian covers of surface singularities (2001)
Neumann, Walter D., Wahl, Jonathan
We discuss the evidence for and implications of a conjecture that the universal abelian cover of a Q-Gorenstein surface singularity with finite local homology (i.e., the singularity link is a...
Hyperplane sections of Calabi-Yau varieties (2001)
Theorem: If W is a smooth complex projective variety with h^1 (O-script_W) = 0, then a sufficiently ample smooth divisor X on W cannot be a hyperplane section of a Calabi-Yau variety, unless W is...
Universal abelian covers of quotient-cusps (2001)
Neumann, Walter D., Wahl, Jonathan
The quotient-cusp singularities are isolated complex surface singularities that are double-covered by cusp singularities. We show that the universal abelian cover of such a singularity, branched only...
On Cohomology of the Square of an Ideal Sheaf (1996)
For a smooth subvariety $X\subset\Bbb P^N$, consider (analogously to projective normality) the vanishing condition $H^1(\Bbb P^N,\Cal I^2_X(k))=0$, $k\ge3$. This condition is shown to be satisfied...