arXiv Open Access 2015

Explicit Brill-Noether-Petri general curves

Enrico Arbarello Andrea Bruno Gavril Farkas Giulia Saccà

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Abstrak

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 $g$.

Topik & Kata Kunci

math.AG

Penulis (4)

Enrico Arbarello

Andrea Bruno

Gavril Farkas

Giulia Saccà

Format Sitasi

APA MLA BibTeX

Arbarello, E., Bruno, A., Farkas, G., Saccà, G. (2015). Explicit Brill-Noether-Petri general curves. https://arxiv.org/abs/1511.07321

Akses Cepat

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Informasi Jurnal

Tahun Terbit: 2015
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓