Timeline for Exceptional divisor of the Hilbert-Chow morphism of the punctual Hilbert scheme
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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 |