Diagonal quartic surfaces with a Brauer–Manin obstruction
T Santens - Compositio Mathematica, 2023 - cambridge.org
Compositio Mathematica, 2023•cambridge.org
In this paper we investigate the quantity of diagonal quartic surfaces which have a Brauer–
Manin obstruction to the Hasse principle. We are able to find an asymptotic formula for the
quantity of such surfaces ordered by height. The proof uses a generalization of a method of
Heath-Brown on sums over linked variables. We also show that there exists no uniform
formula for a generic generator in this family.
Manin obstruction to the Hasse principle. We are able to find an asymptotic formula for the
quantity of such surfaces ordered by height. The proof uses a generalization of a method of
Heath-Brown on sums over linked variables. We also show that there exists no uniform
formula for a generic generator in this family.
In this paper we investigate the quantity of diagonal quartic surfaces which have a Brauer–Manin obstruction to the Hasse principle. We are able to find an asymptotic formula for the quantity of such surfaces ordered by height. The proof uses a generalization of a method of Heath-Brown on sums over linked variables. We also show that there exists no uniform formula for a generic generator in this family.
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