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- W2891600716 abstract "We describe linear algebra algorithms for doing arithmetic on an abelian variety which is dual to a given abelian variety. The ideas are inspired by Khuri-Makdisi’s algorithms for Jacobians of curves. Let $$chi _{0}$$ be the Euler characteristic of the line bundle associated with an ample divisor H on an abelian variety A. The Hilbert scheme of effective divisors D such that $${mathscr {O}}(D)$$ has Hilbert polynomial $$(1+t)^gchi _{0}$$ is a projective bundle (with fibres $${mathbb {P}}^{chi _{0}-1}$$ ) over the dual abelian variety $$widehat{A}$$ via the Abel–Jacobi map. This Hilbert scheme can be embedded in a Grassmannian, so that points on it (and hence, via the above-mentioned Abel–Jacobi map, points on $$widehat{A}$$ ) can be represented by matrices. Arithmetic on $$widehat{A}$$ can be worked out by using linear algebra algorithms on the representing matrices." @default.
- W2891600716 created "2018-09-27" @default.
- W2891600716 creator A5024825185 @default.
- W2891600716 creator A5051026863 @default.
- W2891600716 date "2018-01-01" @default.
- W2891600716 modified "2023-09-26" @default.
- W2891600716 title "Explicit Arithmetic on Abelian Varieties" @default.
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- W2891600716 doi "https://doi.org/10.1007/978-3-319-97379-1_15" @default.
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