Timeline for Divisors on product abelian fourfolds

7 events

when toggle format	what		by	license	comment
May 11 at 11:36	vote	accept	Fra
May 10 at 15:52	answer	added	R. van Dobben de Bruyn		timeline score: 1
May 7 at 11:27	comment	added	Fra		I see. I guess I wasn't precise enough in my question, but I am indeed interested in the complex part of the story, so if you could give me a reference for the well-known argument I would be extremely grateful. Thank you.
May 2 at 20:43	comment	added	R. van Dobben de Bruyn		Hmm, at the time I wrote my dissertation, I did not know a reference for this, so I wrote it up myself (§4.4). Over the complex numbers, there is an easier and pretty well-known argument for $\operatorname{NS}$ using the Lefschetz (1,1)-theorem.
May 2 at 18:32	comment	added	Fra		Thank you! Would you be so kind as to give me a reference for such isomorphism? Maybe it's not hard to prove it but I'd still like to double check.
Apr 30 at 17:32	comment	added	R. van Dobben de Bruyn		The Picard scheme of a product $(X,x) \times (Y,y) = (X \times Y, (x,y))$ of smooth proper pointed varieties $(X,x)$, $(Y,y)$ satisfies $\mathbf{Pic}_{X \times Y} \cong \mathbf{Pic}_X \times \mathbf{Pic}_Y \times \operatorname{Hom}(\mathbf{Alb}_X,\mathbf{Pic}_Y^0)$. This gives a recipe for producing classes in $\operatorname{NS}(A \times A)$: most of the interesting ones come from endomorphisms of $A$.
Apr 30 at 12:58	history	asked	Fra	CC BY-SA 4.0