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Sep 28, 2012 at 16:29 vote accept Johnson-Leung
Sep 28, 2012 at 2:41 answer added Will Sawin timeline score: 5
Sep 28, 2012 at 0:54 comment added Johnson-Leung OK. I edited it to not imply that I have a projective model. Formally applying Weil restriction, I get the surface as the intersection of two affine varieties.
Sep 28, 2012 at 0:53 history edited Johnson-Leung CC BY-SA 3.0
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Sep 28, 2012 at 0:44 comment added Mohan Any complete intersection surface in projective space has $q=0$, so it can not be an Abelian surface.
Sep 28, 2012 at 0:33 comment added Johnson-Leung This is explicit: The Weil restriction of an elliptic curve over a quadratic extension is an abelian surface. Restriction of scalars of the ideal of the curve gives two equations in four variables. I'm not an algebraic geometer, but I think that makes it a complete intersection.
Sep 27, 2012 at 23:49 comment added Piotr Achinger I don't think that an abelian surface can be a complete intersection.
Sep 27, 2012 at 23:27 history asked Johnson-Leung CC BY-SA 3.0