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- W1532133020 abstract "Consider the germ of a plane curve (C0, 0) := V (f) c C2 with an isolated singularityat 0 where f 2 OC2,0. The δ-invariant of (C0, 0) can be interpreted as the maximumnumber of singularities that can pile up on the zero level set of a deformation off. Let F 2 OC2xC;0 be a miniversal deformation of f then the δ-constant stratumD(δ) in the discriminant of F is the set of parameters where the δ-invariant of thedeformed curve is equal to the δ-invariant of the original curve.Givental and Varchenko showed that when (C0, 0) is irreducible, then D(δ) is anexample of a Lagrangian singularity with respect to a symplectic form arising fromthe intersection pairing on the deformed curves. More recently van Straten andSevenheck have developed a theory of deformations of Lagrangian singularities andconjecture that D(δ) is a rigid Lagrangian singularity when (C0, 0) is an irreducibleplane curve singularity.In this thesis we will show how to compute the symplectic form explicitly in thecase of an irreducible simple singularity. Using this symplectic form we constructa maximal Cohen-Macaulay module on the discriminant that can be used to findequations for D(δ) for the A2k,E6 and E8 singularities. We will add weight to theconjecture of van Straten and Sevenheck by showing that D(δ) is Cohen-Macaulayfor E6 and E8." @default.
- W1532133020 created "2016-06-24" @default.
- W1532133020 creator A5077829349 @default.
- W1532133020 date "2011-06-01" @default.
- W1532133020 modified "2023-09-26" @default.
- W1532133020 title "Deformations of plane curve singularities and the δ-constant stratum" @default.
- W1532133020 hasPublicationYear "2011" @default.
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