Explicit Brill-Noether-Petri general curves
| Autor: | Giulia Saccà, Enrico Arbarello, Andrea Bruno, Gavril Farkas |
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| Přispěvatelé: | Arbarello, Enrico, Bruno, Andrea, Farkas, GAVRIL MARIUS, Saccà, Giulia |
| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: |
Degree (graph theory)
Plane curve General Mathematics 010102 general mathematics Moduli of curve 01 natural sciences 14H51 14J28 010101 applied mathematics Combinatorics symbols.namesake Mathematics - Algebraic Geometry Surfaces with canonical section Mathematics::Algebraic Geometry Genus (mathematics) Brill-Noether theory symbols FOS: Mathematics Mathematics (all) Gravitational singularity Brill–Noether theory 0101 mathematics Noether's theorem Algebraic Geometry (math.AG) Mathematics |
| Popis: | Let $p_1,\dots, p_9$ be the points in $\mathbb A^2(\mathbb Q)\subset \mathbb P^2(\mathbb Q)$ with coordinates $$(-2,3),(-1,-4),(2,5),(4,9),(52,375), (5234, 37866),(8, -23), (43, 282), \Bigl(\frac{1}{4}, -\frac{33}{8} \Bigr)$$ respectively. We prove that, for any genus $g$, a plane curve of degree $3g$ having a $g$-tuple point at $p_1,\dots, p_8$, and a $(g-1)$-tuple point at $p_9$, and no other singularities, exists and is a Brill-Noether general curve of genus $g$, while a general curve in that $g$-dimensional linear system is a Brill-Noether-Petri general curve of genus $g$. New section added containing an explicit example of a 9-tuple of points in P^2(Q) that are of 3g-general for every g. Added a second proof of the fact that a du Val curve is BN general. Improved exposition |
| Databáze: | OpenAIRE |
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