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Showing 1 to 3 of 3 for “"genus two curves"”.
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Linear Forms in Logarithms and Integer Points on Genus-two Curves
… at points on the analytic Jacobian of a genus-two curve whose projective coordinates are algebraic. Previous results on the existence of a lower bound of a particular shape are made explicit. We study various properties of Jacobians of genus-two curves, paying particular attention to …
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Computing the Cassels-Tate Pairing for Jacobian Varieties of Genus Two Curves
Let J be the Jacobian variety of a genus two curve defined over a number field K. The main focus of this thesis is on computing the Cassels-Tate pairing on the 2-Selmer group of J. We start by studying the Cassels-Tate pairing when J admits a Richelot isogeny φ : J → J. Suppose all points in J[2] …
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Enumerative algebraic geometry via techniques of symplectic topology and analysis of local obstructions
… methods developed are to enumeration of rational curves with a cusp of specified nature in projective spaces. A general approach for counting positive-genus curves with a fixed complex structure is also presented. The applications described include enumeration of rational curves with a (3,4)-cusp, …