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Feb 18, 2015 at 21:23 comment added Alex Degtyarev What can possibly be simpler? You don't even need logarithmic differentials! And, of course, this is all described in Deligne's three papers very nicely.
Feb 18, 2015 at 20:46 answer added Donu Arapura timeline score: 7
Feb 18, 2015 at 20:43 comment added Mostafa - Free Palestine @AlexDegtyarev You mean to consider the Hodge complex structure on the kernel? Does there exist a simpler way?
Feb 18, 2015 at 20:32 comment added Alex Degtyarev This is even easier than the complement: just consider the kernel of the restriction map $\Omega^*(X)\to\Omega^*(Y)$; it computes what you want and, by Deligne, it has a mixed Hodge structure.
Feb 18, 2015 at 20:19 history asked Mostafa - Free Palestine CC BY-SA 3.0