Algebraic k-systems of curves
| Autor: | Charles Daly, Simran Nayak, Max Lahn, Jonah Gaster, Aisha Mechery |
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| Rok vydání: | 2020 |
| Předmět: |
Surface (mathematics)
010102 general mathematics Intersection number Geometric Topology (math.GT) Algebraic geometry Absolute value (algebra) 01 natural sciences Combinatorics Mathematics - Geometric Topology Differential geometry Simple (abstract algebra) Genus (mathematics) 0103 physical sciences FOS: Mathematics Mathematics - Combinatorics Combinatorics (math.CO) 010307 mathematical physics Geometry and Topology 0101 mathematics Algebraic number Mathematics |
| Zdroj: | Geometriae Dedicata. 209:125-134 |
| ISSN: | 1572-9168 0046-5755 |
| DOI: | 10.1007/s10711-020-00526-6 |
| Popis: | A collection $ \Delta $ of simple closed curves on an orientable surface is an algebraic $ k $-system if the algebraic intersection number $\langle \alpha,\beta \rangle$ is equal to $k $ in absolute value for every $ \alpha , \beta \in \Delta $ distinct. Generalizing a theorem of [MRT14] we compute that the maximum size of an algebraic $k$-system of curves on a surface of genus $g$ is $2g+1$ when $g\ge 3$ or $k$ is odd, and $2g$ otherwise. To illustrate the tightness in our assumptions, we present a construction of curves pairwise geometrically intersecting twice whose size grows as $g^2$. Comment: 7 pages, 2 figures |
| Databáze: | OpenAIRE |
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