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Feb 4, 2011 at 15:45 comment added ginevra86 I think so because the determinant of a a coherent sheaf coincides with the determinant of its double dual. In my case $S$ is smooth and so everythink should work as you wrote. Thank you very much!
Feb 4, 2011 at 15:11 history answered Mike Skirvin CC BY-SA 2.5