Characterizing the Increase of the Residual Order under Blowup in Positive Characteristic
| Autor: | Herwig Hauser, Stefan Perlega |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
General Mathematics
Mathematical analysis Zero (complex analysis) 14B05 14E15 12D10 Resolution of singularities Multiplicity (mathematics) Mathematics - Commutative Algebra Commutative Algebra (math.AC) Residual Mathematics - Algebraic Geometry Hypersurface FOS: Mathematics Ideal (ring theory) Invariant (mathematics) Constant (mathematics) Algebraic Geometry (math.AG) Mathematics |
| Zdroj: | Publications of the Research Institute for Mathematical Sciences. 55:835-857 |
| ISSN: | 0034-5318 |
| DOI: | 10.4171/prims/55-4-7 |
| Popis: | In characteristic zero, the residual order constitutes, after the local multiplicity, the second key invariant for the resolution of singularities. It is defined as the order of the coefficient ideal in a local hypersurface of maximal contact, minus the exceptional multiplicities. It does not increase under blowup in permissible centers as long as the local multiplicity remains constant. In positive characteristic, however, the residual order (defined now as the maximum over all smooth local hypersurfaces) may increase under blowup. In the article we analyze in detail the circumstances when this happens. This may help to develop a modification of the residual order which does work in positive characteristic. Comment: 19 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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