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Dec 4, 2012 at 18:36 vote accept Mike Lowrey
Dec 3, 2012 at 7:33 answer added rita timeline score: 5
Dec 3, 2012 at 7:33 comment added Damian Rössler In this case, $X$ in particular has maximal Albanese dimension. Green-Lazarsfeld ("Deformation theory...", Invent. Math. 90) showed that in this case $(-1)^{{\rm dim}(X)}\chi(X,{\cal O}_X)\geq 0$.
Dec 3, 2012 at 4:19 comment added naf Olivier Debarre has several papers on subvarieties of (simple) abelian varieties which you might find useful/interesting.
Dec 2, 2012 at 18:11 comment added PRL In general h^1,0 >= dim A, but that doesn't use the fact that the map is a closed immersion.
Dec 2, 2012 at 18:09 history asked Mike Lowrey CC BY-SA 3.0