Image Milnor number and đť’śe-codimension for maps between weighted homogeneous irreducible curves
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D. A. H. Ament
Abstract
Let (X, 0) ⊂ (ℂn, 0) be an irreducible weighted homogeneous singularity curve and let f : (X, 0) → (ℂ2, 0) be a finite map germ, one-to-one and weighted homogeneous with the same weights of (X, 0). We show that 𝒜e-codim(X, f) = μI(f), where the 𝒜e-codimension 𝒜e-codim(X, f) is the minimum number of parameters in a versal deformation and μI(f) is the image Milnor number, i.e. the number of vanishing cycles in the image of a stabilization of f.
Communicated by: R. Cavalieri
Funding: The first author has been supported by CAPES. The second author has been partially supported by DGICYT Grant MTM2015–64013–P. The third author is partially supported by CNPq Grant 309086/2017-5 and FAPESP Grant 2016/04740-7.
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© 2020 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Multiprojective witness sets and a trace test
- Image Milnor number and đť’śe-codimension for maps between weighted homogeneous irreducible curves
- Generalizations of 3-Sasakian manifolds and skew torsion
- Uniform modular lattices and affine buildings
- Homogeneous Finsler spaces with exponential metric
- Continuous CM-regularity of semihomogeneous vector bundles
- Solutions to the affine quasi-Einstein equation for homogeneous surfaces
- The geometry of H4 polytopes
Articles in the same Issue
- Frontmatter
- Multiprojective witness sets and a trace test
- Image Milnor number and đť’śe-codimension for maps between weighted homogeneous irreducible curves
- Generalizations of 3-Sasakian manifolds and skew torsion
- Uniform modular lattices and affine buildings
- Homogeneous Finsler spaces with exponential metric
- Continuous CM-regularity of semihomogeneous vector bundles
- Solutions to the affine quasi-Einstein equation for homogeneous surfaces
- The geometry of H4 polytopes
