Timeline for Semistable minimal model of a $K3$-surface and the special fibre
Current License: CC BY-SA 3.0
7 events
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| Nov 20, 2013 at 3:38 | comment | added | Rogelio Yoyontzin | Is is true that if we have a semi-stable minimal model $X\rightarrow \mathop{spec}(R)$ with $R$ a complete discreat valuation ring, with smooth generic fibre a $K3$-surface, then the special fibre $X_0$ (with the induced log structure) is a simple normal crossing Log $K3$-surface? Even if we assume that the special fibre is reduced and that its components are geometrically irreducible why is it $d$-semistable and why $H^1(X_0,\mathcal O_{X_0}) = 0$ and $\Omega_{X_0}^2(log) = \mathcal{O}_{X_0}$? | |
| Nov 20, 2013 at 3:25 | comment | added | Rogelio Yoyontzin | Yes, I have seen that paper. He works on characteristic $p$ and I am on mixed characteristic. Looking at Maulik's arguments on section 4, he claims that having a semi-stable minimal model, then indeed the special fibre is combinatorial, however there is something that I am missing: He said that this follows by Nakkajima, but for Nakkajima we need to have that the special fibre to be a simple normal crossing log K3-surface. Why is it true in Maulik's paper? | |
| Nov 19, 2013 at 10:47 | comment | added | Christian Liedtke | you should have a look at Maulik's paper "Supersingular K3 surfaces for large primes" (arxiv.org/abs/1203.2889), and in particular to Section 4 | |
| Nov 18, 2013 at 17:21 | history | edited | Rogelio Yoyontzin | CC BY-SA 3.0 |
added 198 characters in body; edited tags
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| Nov 18, 2013 at 17:12 | comment | added | Rogelio Yoyontzin | ups… that is right! | |
| Nov 18, 2013 at 17:10 | comment | added | user5117 | Some of your references seem to have ended up in the middle of sentences. Also, "desecrate" should be "discrete". | |
| Nov 18, 2013 at 16:52 | history | asked | Rogelio Yoyontzin | CC BY-SA 3.0 |