Principal analytic link theory in homology sphere links (2009)
Nemethi, A., Neumann, Walter D, Pichon, A.
For the link $M$ of a normal complex surface singularity $(X,0)$ we ask when a knot $K\subset M$ exists for which the answer to whether $K$ is the link of the zero set of some analytic germ $(X,0)\to...
Invariants of open books of links of surface singularities (2009)
In the present article we determine and characterize completely the support genus, the binding number and the norm of a page of an open book under the following restrictions: M is a rational homology...
Equivariant classes of matrix matroid varieties (2008)
Feher, L. M., Nemethi, A., Rimanyi, R.
Consider an integer associated with every subset of the set of columns of an $n\times k$ matrix. The collection of those matrices for which the rank of a union of columns is the predescribed integer...
Spectral Pairs, Mixed Hodge Modules, and Series of Plane Curve Singularities (2008)
Abstract. We consider a mixed Hodge module M on a normal surface singularity (X � x) and a holomorphic function germ f:(X � x) ! (C � 0). For the case that M has an abelian local monodromy...
Spectral Pairs, Mixed Hodge Modules, and Series of Plane Curve Singularities (2008)
Abstract. We consider a mixed Hodge module M on a normal surface singularity (X � x) and a holomorphic function germ f:(X � x) ! (C � 0). For the case that M has an abelian local monodromy...
Milnor open books and Milnor fillable contact 3-manifolds (2007)
Caubel, C., Nemethi, A., Popescu-Pampu, P.
We say that a contact manifold is Milnor fillable if it is contactomorphic to the contact boundary of an isolated complex-analytic singularity (X,x). Generalizing results of Milnor and Giroux, we...
De Bobadilla, J. Fernandez, Luengo, I., Melle-Hernandez, A., Nemethi, A.
It is a very old and interesting open problem to characterize those collections of embedded topological types of local plane curve singularities which may appear as singularities of a projective...
On rational cuspidal curves, open surfaces and local singularities (2006)
De Bobadilla, J. Fernandez, Luengo, I., Melle-Hernandez, A., Nemethi, A.
Let $C$ be an irreducible projective plane curve in the complex projective space ${\mathbb{P}}^2$. The classification of such curves, up to the action of the automorphism group $PGL(3,{\mathbb{C}})$...
The degree of the discriminant of irreducible representations (2005)
Feher, L. M., Nemethi, A., Rimanyi, R.
We present a formula for the degree of the discriminant of irreducible representations of a Lie group, in terms of the roots of the group and the highest weight of the representation. The proof uses...
Milnor open books and Milnor fillable contact 3-manifolds (2004)
Caubel, C., Nemethi, A., Popescu-Pampu, P.
We say that a contact manifold is Milnor fillable if it is contactomorphic to the contact boundary of an isolated complex-analytic singularity (X,x). Generalizing results of Milnor and Giroux, we...
Links and analytic invariants of superisolated singularities (2003)
Luengo-Velasco, I., Melle-Hernandez, A., Nemethi, A.
By using superisolated surface singularities whose link is a rational homology sphere we give counterexamples to some of the most important conjetures concernig invariants of normal surface...
Coincident root loci of binary forms (2003)
Feher, L. M., Nemethi, A., Rimanyi, R.
Coincident root loci are subvarieties of $S^d(C^2)$--the space of binary forms of degree $d$--labelled by partitions of $d$. Given a partition $\lambda$, let $X_\lambda$ be the set of forms with root...
Hypersurface Complements, Alexander Modules and Monodromy (2002)
We consider an arbitrary polynomial map $f:{\mathbb C}^{n+1}\to {\mathbb C} $ and we study the Alexander invariants of ${\mathbb C}^{n+1}\setminus X$ for any fiber $X$ of $f$. The article has two...
On the monodromy at infinity of a polynomial map, II (1996)
In the last years a lot of work has been concentrated on the study of the behaviour at infinity of polynomial maps. This behaviour can be very complicated, therefore the main idea was to find special...