Displaying similar documents to “The geometry of the third moment of exponential sums”

The arithmetic of certain del Pezzo surfaces and K3 surfaces

Dong Quan Ngoc Nguyen (2012)

Journal de Théorie des Nombres de Bordeaux

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We construct del Pezzo surfaces of degree violating the Hasse principle explained by the Brauer-Manin obstruction. Using these del Pezzo surfaces, we show that there are algebraic families of surfaces violating the Hasse principle explained by the Brauer-Manin obstruction. Various examples are given.

Manin’s conjecture for a singular sextic del Pezzo surface

Daniel Loughran (2010)

Journal de Théorie des Nombres de Bordeaux

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We prove Manin’s conjecture for a del Pezzo surface of degree six which has one singularity of type . Moreover, we achieve a meromorphic continuation and explicit expression of the associated height zeta function.

A 4₃ configuration of lines and conics in ℙ⁵

Tomasz Szemberg (1994)

Annales Polonici Mathematici

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Studying the connection between the title configuration and Kummer surfaces we write explicit quadratic equations for the latter. The main results are presented in Theorems 8 and 16.

Density of rational points on cyclic covers of

Ritabrata Munshi (2009)

Journal de Théorie des Nombres de Bordeaux

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We obtain upper bound for the density of rational points on the cyclic covers of . As our estimate tends to the conjectural bound of Serre.