Timeline for Topological self-maps of smooth complex hypersufaces in complex projective spaces

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Nov 17, 2012 at 15:37	comment	added	algori		diverietti -- that's precisely the point: holomorphic endomorphisms of positive degree don't exist (that's what Beauville proves) but continuous do. The way I understand it, aglearner is asking for an explicit construction of such an endomorphism.
Nov 17, 2012 at 12:11	comment	added	diverietti		Hi aglearner, I don't understand your "added"... Proposition 2 of the paper you linked states that if $X$ is a compact manifold, with an endomorphism $f$ of degree $>1$ then the Kodaira dimension $\kappa(X)$ is $<\dim(X)$. But smooth a quintic in $\mathbb P^3$ has ample canonical bundle by adjunction, thus it is of maximal Kodaira dimension.
Nov 17, 2012 at 0:38	history	edited	aglearner	CC BY-SA 3.0	added 183 characters in body
Nov 16, 2012 at 21:56	comment	added	algori		aglearner -- welcome!
Nov 16, 2012 at 16:44	comment	added	algori		.. erm.. that should have been "all except curves of genus $>1$".
Nov 16, 2012 at 16:41	comment	added	algori		aglearner -- as pointed out by Donu Arapura in this thread: mathoverflow.net/questions/112572/…, by a formality argument the answer is "all except curves of genus $\leq 1$"; the argument is applicable since smooth projective hypersurfaces and, more generally, complete intersections are simply-connected unless they are curves by Lefschetz theorem.
Nov 16, 2012 at 14:49	history	edited	aglearner	CC BY-SA 3.0	added 70 characters in body
Nov 16, 2012 at 14:07	history	asked	aglearner	CC BY-SA 3.0