Timeline for What does Hodge theory tell us about simply connected surfaces of general type
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| Jun 8, 2013 at 12:19 | comment | added | Christian Liedtke | actually, the canonical bundle is usually only big and nef, not ample (it is ample on the canonical model). One obvious answer: since $b_1=0$ (first Betti number), we know that the Albanese variety is trivial, i.e., every morphism to an Abelian variety/a torus is trivial. There are plenty of minimal surfaces of general type, and as far as I know, we do not have a good picture at all, even over the simply connected ones. However, being a simply connected 4-manifold, its homeomorphism type is determined by its intersection form (Freedman's theorem), but this has nothing to do with Hodge theory. | |
| Jun 6, 2013 at 13:23 | history | asked | Fabiano Rug | CC BY-SA 3.0 |