Publications - Claus Hertling
Papers
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Analytische Invarianten bei den unimodularen und bimodularen
Hyperflächensingularitäten. Dissertation.
188 Seiten. Bonner Math. Schriften 250 , Bonn 1992.
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Ein Torellisatz füur die unimodalen
und bimodularen Hyperflächensingularitäten.
Math. Ann. 302 (1995), 359--394.
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with Gert-Martin Greuel and Gerhard Pfister: Moduli
spaces of semiquasihomogeneous singularities with fixed principal part.
J. Algebraic Geometry 6 (1997), 169--199.
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Brieskorn lattices and Torelli type
theorems for cubics in P3 and for Brieskorn-Pham
singularities with coprime exponents.
In: Singularities, the Brieskorn anniversary volume
(eds. V.I. Arnold, G.-M. Greuel, J.H.M. Steenbrink),
Progress in Mathematics 162.
Birkhäuser Verlag Basel-Boston-Berlin 1998, 167--194.
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Classifying spaces and moduli spaces
for polarized mixed Hodge structures and for Brieskorn lattices.
Compositio Math. 116 (1999), 1--37.
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with Colin Stahlke: Bernstein polynomial and
Tjurina number. Geometriae Dedicata 75 (1999), 137--176.
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with Yuri Manin: Weak Frobenius manifolds.
International Mathematics Research Notices 1999, No. 6,
277--286.
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Formules pour la multiplicité
et le nombre de Milnor d'un feuilletage sur (C2, 0).
Annales de la Faculté des Sciences de Toulouse IX no.4 (2000),
655--670.
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Variance of the spectral numbers.
In: New developments in singularity theory (ed. D. Siersma
et al.), Kluwer Acad. Publ. Dordrecht-Boston-London 2001, 235--255.
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Frobenius manifolds and
hypersurface singularities, 4 lectures. In:
Real and complex singularities, Proceedings of the VIth workshop at
São Carlos (eds. D. Mond and M.J. Saia),
Lecture Notes in Pure and Applied Mathematics 232 ,
Marcell Decker 2003, 306--332.
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with Hélène Esnault: Semistable bundles on curves
and reducible representations of the fundamental group.
Intern. Journal of Math. 12.7 (2001), 847--855.
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Generic Torelli for semiquasihomogeneous
singularities. In: Trends in singularities (eds. A. Libgober, M. Tibar),
Birkhäuser Verlag Basel 2002, 115--140.
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tt* geometry, Frobenius manifolds,
their connections, and the construction for singularities.
J. reine angew. Math 555 (2003), 77-161.
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with Yuri Manin: Unfoldings of meromorphic
connections and a construction theorem for Frobenius manifolds.
In: Frobenius manifolds, quantum cohomology, and singularities
(eds. C. Hertling and M. Marcolli), Vieweg 2004, 113--144.
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tt* geometry and mixed Hodge structures.
In: Singularity theory and its applications (eds. S. Izumiya et al.),
Advanced Studies in Pure Mathematics 43 ,
Mathematical Society of Japan, 2006, 73--84.
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Formes bilinéaires et hermitiennes pour des singularités:
un apercu. In: Singularités (ed. D. Barlet),
Institut Élie Cartan Nancy 18 , 2005, 1--17.
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Structures tt*.
In: Singularités (ed. D. Barlet), Institut Élie Cartan Nancy
18 , 2005, 47--65.
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with Christian Sevenheck:
Nilpotent orbits of a generalization of Hodge structures.
J. reine angew. Math 609 (2007), 23--80.
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with Christian Sevenheck:
Curvature of classifying spaces for Brieskorn lattices.
Journal of Geometry and Physics 58 (2008), 1591--1606.
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with Christian Sevenheck:
Twistor structures, tt* geometry and singularity theory.
In: From Hodge theory to Integrability and tQFT: tt*-geometry
(eds. R. Donagi and K. Wendland), Proceedings of Symposia in
Pure Mathematics 78 , AMS, 2008, 49--73.
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with Yuri Manin and Constantin Teleman:
An update on semisimple quantum cohomology and F-manifolds.
Proceedings of the Steklov Institute of Mathematics 264
(2009), 62--69.
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with Christian Sevenheck:
Limit of families of Brieskorn lattices and compactified
classifying spaces. Advances in Mathematics 223 (2010), 1155-1224.
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with Luuk Hoevenaars and Hessel Posthuma:
Frobenius manifolds, projective special geometry and Hitchin systems.
J. reine angew. Math. 649 (2010), 117-165.
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with Claude Sabbah:
Examples of non-commutative Hodge structures.
Journal of the Inst. of Math. Jussieu 10(3) (2011), 635-674.
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mu-constant monodromy groups and marked singularities.
Ann. Inst. Fourier, Grenoble 61.7 (2011), 2643-2680.
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with Ralf Kurbel: On the classification of quasihomogeneous singularities.
Journal of Singularities 4 (2012), 131-153.
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with Liana David: Hermitian metrics on F-manifolds.
Journal of Geometry and Physics 107 (2016), 60-78.
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with Falko Gauss: mu-constant monodromy groups and Torelli results
for marked singularities, for the unimodal and some bimodal singularities.
Singularities and Computer Algebra,
Festschrift for Gert-Martin Greuel on the Occasion of his 70th Birthday
(W. Decker, G. Pfister, M. Schulze, eds.). Springer International Publishing
2017, 109-146.
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with Liana David: Unfoldings for regular F-manifolds.
Ann. Sc. Norm. Super. Pisa Cl. Sci (5) Vol. XVII (2017), 1121-1152.
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with Alexander Varchenko: Potentials of a Frobenius like structure.
Glasgow Mathematical Journal 2018, https://doi.org/10.1017/S0017089517000374, 13 pages.
Preliminary longer version arXiv:1608.08423v1, 18 pages.
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with Sven Balnojan: Real Seifert forms and polarizing forms of Steenbrink
mixed Hodge structures. Bull Braz Math Soc, New Series 50.1 (2019),
233-274.
Preprint version arXiv:1712.00383, 42 pages, 01.12.2017.
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with Falko Gauss: mu-constant monodromy groups and Torelli results
for the quadrangle singularities and the bimodal series.
Journal of Singularities 18 (2018), 119-215.
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Automorphisms with eigenvalues in S1 of a Z-lattice
with cyclic finite monodromy.
Acta Arithmetica, 2019, DOI: 10.4064/aa180125-7-12, 30 pages.
Preprint version arXiv:1801.07924, 33 pages, 24.01.2018.
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with Philip Zilke: Seven combinatorial problems around quasihomogeneous
singularities.
Journal of Algebraic Combinatorics, 2019, https://doi.org/10.1007/s10801-018-0864-9,
36 pages. Preprint version arXiv:1801.08272, 37 pages, 25.01.2018.
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with Sven Balnojan: Reduced and nonreduced presentations of Weyl group
elements.
Journal of Lie theory 29.2 (2019), 559-599.
Preprint version arXiv:1604.07967, 49 pages, 27.04.2016.
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with Liana David:
(T)-structures over 2-dimensional F-manifolds: formal classification.
Annali di Matematica Pura ed Applicata, 2019,
https://doi.org/10.1007/s10231-019-00919-9, 22 pages.
Preprint version arXiv:1811.03406v2, 28 pages, 16.07.2019.
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with Céline Roucairol:
Distinguished bases and Stokes regions for the simple and the
simple elliptic singularities. Accepted for publication in a proceedings volume.
Preprint version arXiv:1806.00996, 77 pages, 04.06.2018.
Two books and a Snapshot
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Frobenius manifolds and moduli spaces for singularities.
Cambridge Tracts in Mathematics 151, Cambridge University Press 2002,
270 pages
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with Martin A. Guest: Painlevé III:
a case study in the geometry of meromorphic connections.
Springer Lecture Notes in Mathematics 2198, 2017.
In the arXiv under the following title:
The Painlevé III equation of type (0,0,4,-4),
its associated vector bundles with isomonodromic connections,
and the geometry of the movable poles.
arXiv: 1501.0481v1, 206 pages, 20.01.2015.
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Geometry behind one of the Painlevé III differential equations.
Snapshots of modern mathematics from Oberwolfach, SNAP-2018-010-EN, 15 pages.
Preprints
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with Thomas Brélivet: Bernoulli moments of spectral numbers
and Hodge numbers. Prépublication de'l
Institut Élie Cartan, UHP Nancy 1, 2004/21.
math.AG/0405501. 35 pages.
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with Ralf Kurbel:
Tables of weight systems of quasihomogeneous singularities 15.08.2011.
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with Sven Balnojan: Conjectures on spectral numbers for upper triangular
matrices and for singularities. arXiv:1712.00388, 54 pages, 01.12.2017.