On the brauer group of a designularization of a normal surface¹

¹Mathematics Subject Classification, Primary 13.420, Secondary 16HO5,14F20,14399.

Abstract

If ‰ : ś S → is a desingularization of the norm3 surface S, then it is shown that the induced map H² _et:(S, G_m) → H^2: _et(ś, G_m) is surjective. It

follows that if all of the singularities of S are rational, the Brauer group

map B(S) → B(ś) is surjective. An example is given to show that this

property fails if the dimension of S ≥ 3.

¹Mathematics Subject Classification, Primary 13.420, Secondary 16HO5,14F20,14399.

²2 Supported in part by the NSF under grant DMS-8822944.

¹Mathematics Subject Classification, Primary 13.420, Secondary 16HO5,14F20,14399.

²2 Supported in part by the NSF under grant DMS-8822944.

Notes

¹Mathematics Subject Classification, Primary 13.420, Secondary 16HO5,14F20,14399.

²2 Supported in part by the NSF under grant DMS-8822944.