## 56 Citations

### Brill-Noether problem on splice quotient singularities and duality of topological Poincar\'e series

- Mathematics
- 2021

In this manuscript we investigate the analouge of the Brill-Noether problem for smooth curves in the case of normal surface singularities. We determine the maximal possible value of h of line bundles…

### Combinatorial duality for Poincaré series, polytopes and invariants of plumbed 3-manifolds

- MathematicsSelecta Mathematica
- 2019

Assume that the link of a complex normal surface singularity is a rational homology sphere. Then its Seiberg–Witten invariant can be computed as the ‘periodic constant’ of the topological…

### Combinatorial duality for Poincaré series, polytopes and invariants of plumbed 3-manifolds

- MathematicsSelecta Mathematica
- 2019

Assume that the link of a complex normal surface singularity is a rational homology sphere. Then its Seiberg–Witten invariant can be computed as the ‘periodic constant’ of the topological…

### The Abel map for surface singularities II. Generic analytic structure

- MathematicsAdvances in Mathematics
- 2020

### Geometry of splice-quotient singularities

- Mathematics
- 2008

We obtain a new important basic result on splice-quotient singularities in an elegant combinatorial-geometric way: every level of the divisorial filtration of the ring of functions is generated by…

### Lattice cohomology and Seiberg-Witten invariants of normal surface singularities

- Mathematics
- 2013

One of the main questions in the theory of normal surface singularities is to understand the relations between their geometry and topology. The lattice cohomology is an important tool in the study of…

### Analytic lattice cohomology of surface singularities

- Mathematics
- 2021

We construct the analytic lattice cohomology associated with the analytic type of any complex normal surface singularity. It is the categorification of the geometric genus of the germ, whenever the…

### Seiberg–Witten Invariant of the Universal Abelian Cover of \({S_{-p/q}^{3}(K)}\)

- Mathematics
- 2017

We prove an additivity property for the normalized Seiberg–Witten invariants with respect to the universal abelian cover of those 3-manifolds, which are obtained via negative rational Dehn surgeries…

### On Poincaré series associated with links of normal surface singularities

- MathematicsTransactions of the American Mathematical Society
- 2019

We study the counting function of topological Poincar\'e series associated with rational homology sphere plumbed 3-manifold with connected negative definite tree, interpreting as an alternating sum…

### Local tropicalizations of splice type surface singularities

- Mathematics
- 2021

Splice type surface singularities were introduced by Neumann and Wahl as a generalization of the class of Pham-Brieskorn-Hamm complete intersections of dimension two. Their construction depends on a…

## References

SHOWING 1-10 OF 41 REFERENCES

### Line bundles associated with normal surface singularities

- Mathematics
- 2003

Recently L. Nicolaescu and the author formulated a conjecture which relates the geometric genus of a complex analytic normal surface singularity (whose link $M$ is a rational homology sphere) with…

### Geometry of splice-quotient singularities

- Mathematics
- 2008

We obtain a new important basic result on splice-quotient singularities in an elegant combinatorial-geometric way: every level of the divisorial filtration of the ring of functions is generated by…

### Complete intersection singularities of splice type as universal abelian covers

- Mathematics
- 2004

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…

### Topology, geometry, and equations of normal surface singularities

- Mathematics
- 2005

Abstract In continuing joint work with Walter Neumann, we consider the relationship between three different points of view in describing a (germ of a) complex normal surface singularity. The explicit…

### Surgery formula for Seiberg–Witten invariants of negative definite plumbed 3-manifolds

- Mathematics
- 2007

Abstract We derive a cut-and-paste surgery formula of Seiberg–Witten invariants for negative definite plumbed rational homology 3-spheres. It is similar to (and motivated by) Okuma's recursion…

### Poincaré series of a rational surface singularity

- Mathematics
- 2004

Recently there was found a new method to compute the (generalized) Poincare series of some multi-index filtrations on rings of functions. First the authors had elaborated it for computing the…

### Seiberg-Witten invariants and surface singularities

- Mathematics
- 2002

We formulate a very general conjecture relating the analytical invariants of a normal surface singularity to the Seiberg{Witten invariants of its link provided that the link is a rational homology…

### Complex surface singularities with integral homology sphere links

- Mathematics
- 2005

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…

### The geometric genus of splice-quotient singularities

- Mathematics
- 2006

. We prove a formula for the geometric genus of splice-quotient singularities (in the sense of Neumann and Wahl). This formula enables us to compute the invariant from the resolution graph; in fact,…

### Universal Abelian covers of rational surface singularities and multi-index filtrations

- Mathematics
- 2007

In previous papers, the authors computed the Poincaré series of some (multi-index) filtrations on the ring of germs of functions on a rational surface singularity. These Poincaré series were…