Real algebraic surfaces with many handles in $(\mathbb{CP}^1)^3$
| Autor: | Renaudineau, Arthur |
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| Rok vydání: | 2015 |
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| Druh dokumentu: | Working Paper |
| Popis: | In this text, we study Viro's conjecture and related problems for real algebraic surfaces in $(\mathbb{CP}^1)^3$. We construct a counter-example to Viro's conjecture in tridegree $(4,4,2)$ and a family of real algebraic surfaces of tridegree $(2k,2l,2)$ in $(\mathbb{CP}^1)^3$ with asymptotically maximal first Betti number of the real part. To perform such constructions, we consider double covers of blow-ups of $(\mathbb{CP}^1)^2$ and we glue singular curves with special position of the singularities adapting the proof of Shustin's theorem for gluing singular hypersurfaces. Comment: 29 pages, 8 figures |
| Databáze: | arXiv |
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