Publications - Claus Hertling - August 2022


  1. Analytische Invarianten bei den unimodularen und bimodularen Hyperflächensingularitäten. Dissertation. 188 Seiten. Bonner Math. Schriften 250 , Bonn 1992.

  2. Ein Torellisatz für die unimodalen und bimodularen Hyperflächensingularitäten. Math. Ann. 302 (1995), 359--394.

  3. with Gert-Martin Greuel and Gerhard Pfister: Moduli spaces of semiquasihomogeneous singularities with fixed principal part. J. Algebraic Geometry 6 (1997), 169--199.

  4. 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.

  5. Classifying spaces and moduli spaces for polarized mixed Hodge structures and for Brieskorn lattices. Compositio Math. 116 (1999), 1--37.

  6. with Colin Stahlke: Bernstein polynomial and Tjurina number. Geometriae Dedicata 75 (1999), 137--176.

  7. with Yuri Manin: Weak Frobenius manifolds. International Mathematics Research Notices 1999, No. 6, 277--286.

  8. 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.

  9. 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.

  10. 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.

  11. with Hélène Esnault: Semistable bundles on curves and reducible representations of the fundamental group. Intern. Journal of Math. 12.7 (2001), 847--855.

  12. Generic Torelli for semiquasihomogeneous singularities. In: Trends in singularities (eds. A. Libgober, M. Tibar), Birkhäuser Verlag Basel 2002, 115--140.

  13. tt* geometry, Frobenius manifolds, their connections, and the construction for singularities. J. reine angew. Math 555 (2003), 77-161.

  14. 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.

  15. 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.

  16. Formes bilinéaires et hermitiennes pour des singularités: un apercu. In: Singularités (ed. D. Barlet), Institut Élie Cartan Nancy 18 , 2005, 1--17. English translation on the arXiv: Bilinear forms and hermitian forms for singularities: a survey. arXiv:2011, 21 pages, 19.11.2020.

  17. Structures tt*. In: Singularités (ed. D. Barlet), Institut Élie Cartan Nancy 18 , 2005, 47--65.

  18. with Christian Sevenheck: Nilpotent orbits of a generalization of Hodge structures. J. reine angew. Math 609 (2007), 23--80.

  19. with Christian Sevenheck: Curvature of classifying spaces for Brieskorn lattices. Journal of Geometry and Physics 58 (2008), 1591--1606.

  20. 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.

  21. 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.

  22. with Christian Sevenheck: Limit of families of Brieskorn lattices and compactified classifying spaces. Advances in Mathematics 223 (2010), 1155-1224.

  23. with Luuk Hoevenaars and Hessel Posthuma: Frobenius manifolds, projective special geometry and Hitchin systems. J. reine angew. Math. 649 (2010), 117-165.

  24. with Claude Sabbah: Examples of non-commutative Hodge structures. Journal of the Inst. of Math. Jussieu 10(3) (2011), 635-674.

  25. mu-constant monodromy groups and marked singularities. Ann. Inst. Fourier, Grenoble 61.7 (2011), 2643-2680.

  26. with Ralf Kurbel: On the classification of quasihomogeneous singularities. Journal of Singularities 4 (2012), 131-153.

  27. with Liana David: Hermitian metrics on F-manifolds. Journal of Geometry and Physics 107 (2016), 60-78.

  28. with Falko Gauss: mu-constant monodromy groups and Torelli results for marked singularities, for the unimodal and some bimodal singularities. In: 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.

  29. with Liana David: Unfoldings for regular F-manifolds. Ann. Sc. Norm. Super. Pisa Cl. Sci (5) Vol. XVII (2017), 1121-1152.

  30. with Alexander Varchenko: Potentials of a Frobenius like structure. Glasgow Mathematical Journal 60.3 (2018), 681-693. Preliminary longer version arXiv:1608.08423v1, 18 pages, 30.06.2016.

  31. 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.

  32. 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.

  33. with Philip Zilke: Seven combinatorial problems around quasihomogeneous singularities. Journal of Algebraic Combinatorics 50 (2019), 447-482.

  34. with Sven Balnojan: Reduced and nonreduced presentations of Weyl group elements. Journal of Lie theory 29.2 (2019), 559-599.

  35. Automorphisms with eigenvalues in S1 of a Z-lattice with cyclic finite monodromy. Acta Arithmetica, 192.1 (2020), 1-30.

  36. with Liana David: (T)-structures over 2-dimensional F-manifolds: formal classification. Annali di Matematica Pura ed Applicata (1923 -) 199 (2020), 1221-1242.

  37. with Thomas Brélivet: Bernoulli moments of spectral numbers and Hodge numbers. Journal of Singularities 20 (2020), 205-231.

  38. with Sven Balnojan: Conjectures on spectral numbers for upper triangular matrices and for singularities. Math Phys Anal Geom (2020) 23:5 ., arXiv:1712.00388v1, 54 pages, 01.12.2017.

  39. with Céline Roucairol: Distinguished bases and Stokes regions for the simple and the simple elliptic singularities. In: Moduli spaces and locally symmetric spaces (eds Li-Zhen Ji, Shing-Tung Yau), Surveys of Modern Mathematics 16, Higher Education Press and International Press, Beijing-Boston, 2021, 39-106.

  40. with Liana David: Meromorphic Connections over F-manifolds. In: Integrability, Quantization, and Geometry, I. Integrable systems (eds I. Krichever, S. Novikov, O. Ogievetsky, S. Shlosman), Proceedings of Symposia in Pure Mathematics 103.1, AMS, 171-216.

  41. with Liana David: (TE)-structures over the irreducible 2-dimensional globally nilpotent F -manifold germ. Rev. Roumaine Math. Pures Appl. 65 (2020), 235-284.

  42. with Alexey Basalaev: 3-dimensional F-manifolds. Letters in Mathematical Physics (2021) 111:90 , 50 pages.

  43. with Makiko Mase: The integral monodromy of isolated quasihomogeneous singularities. Algebra and Number Theory 16.4 (2022), 955-1024.

  44. with Makiko Mase: The integral monodromy of the cycle type singularities. Accepted for publication in the Journal of Singularities. Preprint version arXiv:2009.07533v1, 38 pages, 16.09.2020.

  45. Rank 2 bundles with meromorphic connections with poles of Poincaré rank 1. SIGMA 17 (2021), 082, 73 pages. Also arXiv:2009.14314v2.

  46. with Makiko Mase: The combinatorics of weight systems and characteristic polynomials of isolated quasihomogeneous singularities. Journal of Algebraic Combinatorics (2022), published online at .

Two books, a Snapshot, and some tables online