41 citations · 159 across the 39 of their papers we have counts for
27 papers · 1 filter
Algebraic curves and foliations
César Camacho, Hossein Movasati
Consider a field of characteristic , not necessarily algebraically closed, and a fixed algebraic curve defined by a tame polynomial with only quasi-homog…
Bilinear forms and hermitian forms for singularities: a survey
Claus Hertling
The paper collects different approaches and viewpoints on bilinear forms and hermitian forms around isolated hypersurface singularities. It gives the relations between them in prec…
The integral monodromy of isolated quasihomogeneous singularities
Claus Hertling, Makiko Mase
The integral monodromy on the Milnor lattice of an isolated quasihomogeneous singularity is subject of an almost untouched conjecture of Orlik from 1972. We prove this conjecture f…
Rank 2 Bundles with Meromorphic Connections with Poles of Poincaré Rank 1
Claus Hertling
Holomorphic vector bundles on , a complex manifold, with meromorphic connections with poles of Poincaré rank 1 along arise naturally in algeb…
Distinguished bases and Stokes regions for the simple and the simple elliptic singularities
Claus Hertling, Céline Roucairol
Isolated hypersurface singularities come equipped with a Milnor lattice, a -lattice of finite rank, and a set of -bases of this lattice. U…
Potentials of a Frobenius like structure
Claus Hertling, Alexander Varchenko
This paper proves the existence of potentials of the first and second kind of a Frobenius like structure in a frame which encompasses families of arrangements. The frame uses the n…
Conjectures on spectral numbers for upper triangular matrices and for singularities
Sven Balnojan, Claus Hertling
Cecotti and Vafa proposed in 1993 a beautiful idea how to associate spectral numbers to real upper triangular matrices with 1's on the d…
Real Seifert forms and polarizing forms of Steenbrink mixed Hodge structures
Sven Balnojan, Claus Hertling
An isolated hypersurface singularity comes equipped with many different pairings on different spaces, the intersection form and the Seifert form on the Milnor lattice, a polarizing…
-constant monodromy groups and Torelli results for the quadrangle singularities and the bimodal series
Falko Gauss, Claus Hertling
This paper is a sequel to [He11] and [GH17]. In [He11] a notion of marking of isolated hypersurface singularities was defined, and a moduli space for marked singulariti…
Potentials of a Frobenius like structure and bases of a vector space
Claus Hertling, Alexander Varchenko
This paper proves the existence of potentials of the first and second kind of a Frobenius like structure in a frame which encompasses families of arrangements. Surprisingly the pro…
-constant monodromy groups and Torelli results for marked singularities, for the unimodal and some bimodal singularities
Falko Gauss, Claus Hertling
This paper is a sequel to [He7]. There a notion of marking of isolated hypersurface singularities was defined, and a moduli space for marked singularities in one -ho…
The Painlevé III equation of type (0,0,4,-4), its associated vector bundles with isomonodromic connections, and the geometry of the movable poles
Martin A. Guest, Claus Hertling
The paper is about a Painlevé III equation and its relation to isomonodromic families of vector bundles on P^1 with meromorphic connections. The purpose of the paper is two-fold: i…
mu-constant monodromy groups and marked singularities
Claus Hertling
mu-constant families of holomorphic function germs with isolated singularities are considered from a global perspective. First, a monodromy group from all families which contain a…
On the classification of quasihomogeneous singularities
Claus Hertling, Ralf Kurbel
The motivation for this paper are computer calculations of complete lists of weight systems of quasihomogeneous polynomials with isolated singularity at 0 up to rather large Milnor…
Examples of non-commutative Hodge structures
Claus Hertling, Claude Sabbah
We show that if the Stokes matrix of a connection with a pole of order two and no ramification gives rise, when added to its adjoint, to a positive semi-definite Hermitian form, th…
Frobenius manifolds, projective special geometry and Hitchin systems
Claus Hertling, Luuk Hoevenaars, Hessel Posthuma
We consider the construction of Frobenius manifolds associated to projective special geometry and analyse the dependence on choices involved. In particular, we prove that the under…
Twistor structures, tt*-geometry and singularity theory
Claus Hertling, Christian Sevenheck
We give an overview on the tt*-geometry defined for isolated hypersurface singularities and tame functions via Brieskorn lattices. We discuss nilpotent orbits in this context, as w…
Limits of families of Brieskorn lattices and compactified classifying spaces
Claus Hertling, Christian Sevenheck
We investigate variations of Brieskorn lattices over non-compact parameter spaces, and discuss the corresponding limit objects on the boundary divisor. We study the associated vari…
An update on semisimple quantum cohomology and F-manifolds
C. Hertling, Yu. Manin, C. Teleman
In the first section of this note we show that the Theorem 1.8.1 of Bayer--Manin ([BaMa]) can be strengthened in the following way: {\it if the even quantum cohomology of a project…
Curvature of classifying spaces for Brieskorn lattices
Claus Hertling, Christian Sevenheck
We study tt*-geometry on the classifying space for regular singular TERP-structures, e.g., Fourier-Laplace transformations of Brieskorn lattices of isolated hypersurface singularit…
Nilpotent orbits of a generalization of Hodge structures
Claus Hertling, Christian Sevenheck
We study a generalization of Hodge structures which first appeared in the work of Cecotti and Vafa. It consists of twistors, that is, holomorphic vector bundles on P^1, with additi…
Bernoulli moments of spectral numbers and Hodge numbers
Thomas Brélivet, Claus Hertling
The distribution of the spectral numbers of an isolated hypersurface singularity is studied in terms of the Bernoulli moments. These are certain rational linear combinations of the…
Unfoldings of meromorphic connections and a construction of Frobenius manifolds
Claus Hertling, Yuri Manin
The existence of universal unfoldings of certain germs of meromorphic connections is established. This is used to prove a general construction theorem for Frobenius manifolds. A pa…
tt* geometry, Frobenius manifolds, their connections, and the construction for singularities
Claus Hertling
The base space of a semiuniversal unfolding of a hypersurface singularity carries a rich geometry. By work of K. Saito and M. Saito is can be equipped with the structure of a Frobe…