Location of Repository

Linear free divisors and Frobenius manifolds

By Ignacio de Gregorio, D. (David) Mond and Christian Sevenheck


We study linear functions on fibrations whose central fibre is a linear free divisor. We analyse the Gauß–Manin system associated to these functions, and prove the existence of a primitive and homogenous form. As a consequence, we show that the base space of the semi-universal unfolding of such a function carries a Frobenius manifold structure

Topics: QA
Publisher: Cambridge University Press
Year: 2009
OAI identifier: oai:wrap.warwick.ac.uk:2570

Suggested articles



  1. (1977). A classi of irreducible prehomogeneous vector spaces and their relative invariants,
  2. (2009). A construction of Frobenius manifolds with logarithmic poles and applications, doi
  3. (1996). A mirror theorem for toric complete intersections, in Topological theory, primitive forms and related topics (Kyoto, doi
  4. (2007). Asymptotic behaviour of tame harmonic bundles and an application to pure twistor D-modules, Part 1, doi
  5. (1953). Cohomology of Lie algebras, doi
  6. (2005). Construction de vari et es de Frobenius via les polyn^ omes de Laurent: une autre approche,
  7. (1986). Deformations of dierential systems.
  8. (2002). Frobenius manifolds and moduli spaces for singularities, doi
  9. (2004). Gauss Manin systems, Brieskorn lattices and Frobenius structures. II, in Frobenius manifolds, eds C. Hertling doi
  10. (2003). Gauss{Manin systems, Brieskorn lattices and Frobenius structures. doi
  11. (1993). Geometry of 2D topological theories, in Integrable systems and quantum groups. Lectures given at the 1st session of the Centro Internazionale Matematico Estivo (CIME) held in Montecatini
  12. (2009). Good bases for some linear free divisors associated to quiver representations,
  13. (1969). Hautes
  14. (2003). Hertling, tt-geometry, Frobenius manifolds, their connections, and the construction for singularities, doi
  15. (1995). Homological geometry and mirror symmetry,
  16. (2006). Hypergeometric periods for a tame polynomial,
  17. (2007). Isomonodromic deformations and Frobenius manifolds, Universitext (Springer, doi
  18. (2006). Linear free divisors and quiver representations, in Singularities and computer algebra, doi
  19. (2009). Linear free divisors and the global logarithmic comparison theorem, doi
  20. (1988). Milnor numbers and the topology of polynomial hypersurfaces, doi
  21. (2007). Nilpotent orbits of a generalization of Hodge structures, doi
  22. (2006). On the legacy of free divisors. III. Functions and divisors on complete intersections, doi
  23. (1989). On the structure of Brieskorn lattice, doi
  24. (2008). Orbifold quantum cohomology of weighted projective spaces, doi
  25. (2000). Semi-in Hodge structures and mirror symmetry for projective spaces,
  26. (2004). Sheaves in topology (Springer, doi
  27. (2005). Singular 3.0, A computer algebra system for polynomial computations,
  28. (2007). Some examples of non-massive Frobenius manifolds in singularity theory, doi
  29. (1999). Stokes matrices and monodromy of the quantum cohomology of projective spaces, doi
  30. (2009). The Quantum Orbifold Cohomology of weighted projective spaces, doi
  31. (1980). Tokyo Sect.
  32. (2004). Unfoldings of meromorphic connections and a construction of Frobenius manifolds, in Frobenius manifolds, eds C. Hertling doi
  33. (1982). Vari et es polaires. II. Multiplicit es polaires, sections planes, et conditions de Whitney, doi

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.