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Rational points of bounded height on Del Pezzo surfaces of degree six

1995

Let K be a number field. Dénote by V3 a split Del Pezzo surface of degree six over K and by o) its canonical divisor. Dénote by W3 the open complément of the exceptional Unes in K3. Let NWs(-w, X) be the number of ^-rational points on W3 whose anticanonical height H.a is bounded by X. Manin has conjectured that asymptotically NW3(co, X) tends to cX(\o% X)3, where c is a constant depending only on the number field and on the normalization of the height. Our goal is to prove the following

doi:10.5169/seals-53005
fatcat:wa6muzhqcng4fjomi7hjjgdily