Polar exploration of complex surface germs
| Autor: | da Silva, André Belotto, Fantini, Lorenzo, Némethi, András, Pichon, Anne |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Trans. Amer. Math. Soc. 375 (2022), no. 9, 6747--6767 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1090/tran/8749 |
| Popis: | We prove that the topological type of a normal surface singularity $(X,0)$ provides finite bounds for the multiplicity and polar multiplicity of $(X,0)$, as well as for the combinatorics of the families of generic hyperplane sections and of polar curves of the generic plane projections of $(X,0)$. A key ingredient in our proof is a topological bound of the growth of the Mather discrepancies of $(X,0)$, which allows us to bound the number of point blowups necessary to achieve factorization of any resolution of $(X,0)$ through its Nash transform. This fits in the program of polar explorations, the quest to determine the generic polar variety of a singular surface germ, to which the final part of the paper is devoted. Comment: 20 pages, 3 figures. arXiv admin note: text overlap with arXiv:2006.01773 |
| Databáze: | arXiv |
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