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Some problems on Lagrangian singularities. (English) Zbl 1103.14004
Lossen, Christoph (ed.) et al., Singularities and computer algebra. Selected papers of the conference, Kaiserslautern, Germany, October 18–20, 2004 on the occasion of Gert-Martin Greuel’s 60th birthday. Cambridge: Cambridge University Press (ISBN 0-521-68309-2/pbk). London Mathematical Society Lecture Note Series 324, 333-349 (2006).
This is a review of some results concerning Lagrangian varieties, mainly their algebraic and geometric aspects. There are examples of known Lagrangian singularities and their vanishing ideals. Deformations of Lagrangian singularity $$L$$ (and its rigidity) are studied by the complex associated with an involutive ideal and the symplectic structure on the deformation space defined by the intersection form of a Milnor fibre. The $$\delta$$-invariant of a plane curve singularity is studied in the symplectic context which consider the symplectic structure on the Lagrangian deformation space. Finally, the author reports not only on well known basic results but also on some newer developments, and poses some open problems and conjectures.
For the entire collection see [Zbl 1086.14001].

##### MSC:
 14B05 Singularities in algebraic geometry 14B12 Local deformation theory, Artin approximation, etc. 32S40 Monodromy; relations with differential equations and $$D$$-modules (complex-analytic aspects) 32S30 Deformations of complex singularities; vanishing cycles