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Jul 24, 2020 at 12:22 comment added abx If $\pi :Y\rightarrow Z$ is a double covering of smooth varieties, we have $\pi _*\mathscr{O}_Y\cong \mathscr{O}_Z\oplus L^{-1}$ and the multiplication $L^{-1}\otimes L^{-1}\rightarrow \mathscr{O}_Z$ is given by a section of $L^2$, whose divisor is the branch locus.
Jul 24, 2020 at 10:58 answer added ssx timeline score: 1
Jun 9, 2018 at 23:44 comment added Rex @Frank: Thanks. I think equation (2.1.22), and Proposition 2.2 might be relevant to my question.
Jun 9, 2018 at 21:16 comment added Frank I would imagine the original reference for this is one of Fogarty's Hilbert scheme papers, or Beauville's article (in French) which constructs higher dimensional examples of hyperkähler manifolds. You can find a more modern account in O'Grady's notes here irma.math.unistra.fr/~pacienza/notes-ogrady.pdf (see 2.1.22).
Jun 8, 2018 at 23:23 history edited Rex CC BY-SA 4.0
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Jun 8, 2018 at 22:50 history asked Rex CC BY-SA 4.0