The Complete Intersection Discrepancy of a Curve I: Numerical Invariants
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915916813434880 |
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| author | Benguş-Lasnier, Andrei Rangachev, Antoni |
| author_facet | Benguş-Lasnier, Andrei Rangachev, Antoni |
| contents | We generalize two classical formulas for complete intersection curves by introducing the the complete intersection discrepancy of a curve as a correction term. The first is a well-known multiplicity formula in singularity theory, due to Lê, Greuel and Teissier, which relates some of the basic invariants of a curve singularity. We apply this generalization elsewhere to the study of equisingularity of curves. The second is the genus--degree formula for projective curves. The main technical tool used to obtain these generalizations is an adjunction-type identity derived from Grothendieck duality theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_09362 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Complete Intersection Discrepancy of a Curve I: Numerical Invariants Benguş-Lasnier, Andrei Rangachev, Antoni Algebraic Geometry 14B07, 14C17, 14H20, 14H50, 14M06, 13C40, 13H15 We generalize two classical formulas for complete intersection curves by introducing the the complete intersection discrepancy of a curve as a correction term. The first is a well-known multiplicity formula in singularity theory, due to Lê, Greuel and Teissier, which relates some of the basic invariants of a curve singularity. We apply this generalization elsewhere to the study of equisingularity of curves. The second is the genus--degree formula for projective curves. The main technical tool used to obtain these generalizations is an adjunction-type identity derived from Grothendieck duality theory. |
| title | The Complete Intersection Discrepancy of a Curve I: Numerical Invariants |
| topic | Algebraic Geometry 14B07, 14C17, 14H20, 14H50, 14M06, 13C40, 13H15 |
| url | https://arxiv.org/abs/2504.09362 |