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Most binary forms come from a pencil of quadrics
- Source :
- Proceedings of the American Mathematical Society, Series B. 3:18-27
- Publication Year :
- 2016
- Publisher :
- American Mathematical Society (AMS), 2016.
-
Abstract
- A pair of symmetric bilinear forms A and B determine a binary form $f(x,y) = disc(Ax-By)$. We prove that the question of whether a given binary form can be written in this way as a discriminant form generically satisfies a local-global principle and deduce from this that most binary forms over $\mathbf{Q}$ are discriminant forms. This is related to the arithmetic of the hyperelliptic curve $z^2 = f(x,y)$. Analogous results for non-hyperelliptic curves are also given.<br />Comment: v3: updated references
Details
- ISSN :
- 23301511
- Volume :
- 3
- Database :
- OpenAIRE
- Journal :
- Proceedings of the American Mathematical Society, Series B
- Accession number :
- edsair.doi.dedup.....8afc2abd5e131e5959c58369c2bbfb2a