bio | website | |
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location | Montreal | |
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visits | member for | 2 years, 7 months |
seen | 2 days ago | |
stats | profile views | 213 |
Dec 5 |
revised |
Deformation over small disk and deformation over complex disk
added 1 characters in body |
Nov 20 |
comment |
Semistable minimal model of a $K3$-surface and the special fibre
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 |
comment |
Semistable minimal model of a $K3$-surface and the special fibre
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 18 |
revised |
Semistable minimal model of a $K3$-surface and the special fibre
added 198 characters in body; edited tags |
Nov 18 |
comment |
Semistable minimal model of a $K3$-surface and the special fibre
ups… that is right! |
Nov 18 |
asked | Semistable minimal model of a $K3$-surface and the special fibre |
Oct 14 |
comment |
Deformation over small disk and deformation over complex disk
I just change it. I hope it makes more sense now. Thanks. |
Oct 14 |
revised |
Deformation over small disk and deformation over complex disk
deleted 157 characters in body |
Oct 12 |
comment |
Deformation over small disk and deformation over complex disk
You are right Marguax. This is not the condition I want. I will modify (correct) my question tomorrow on my computer. Thanks. |
Oct 12 |
comment |
Deformation over small disk and deformation over complex disk
Yes it is smooth outside the central fibre. I will take a look of SGA 1 to see if this is what I was looking for. Thanks. |
Oct 12 |
comment |
Deformation over small disk and deformation over complex disk
By $X(\mathbb C)$ we understand the $\mathbb C$ points of $X$. We can give to it a structure of complex analytic space. So indeed $X_{an}=X(\mathbb C)$. |
Oct 10 |
asked | Deformation over small disk and deformation over complex disk |
Aug 7 |
accepted | Existence of logarithmic structures and d-semistability |
Aug 7 |
asked | Existence of logarithmic structures and d-semistability |
Aug 5 |
revised |
Torelli-like theorem for K3 surfaces on terms of its étale cohomology
edited title |
Aug 5 |
comment |
Torelli-like theorem for K3 surfaces on terms of its étale cohomology
I meant $H^2_{et}(X,\mathbb Z_p)$ on my previews comment. |
Aug 5 |
comment |
Minimal semistable model for K3-surfaces.
Your are right. |
Aug 5 |
comment |
Torelli-like theorem for K3 surfaces on terms of its étale cohomology
Thanks Matt. This paper of Ogus is good reference! I agree that the result may not be true just as I stayed. What I am looking for is a characterization of K3-surfaces in terms of its p-adic representations. If we Tensor $H^2(X,\mathbb Z)$ with $B_{dR}$ or $B_{HT}$ or $B_{st}$ etc.. we get different extra structures (Like Frobenius, monodromy, Filtrations etc…). It may not exist a result, but I was wondering if we can get something asking a morphism to preserve filtrations, or Frobenius or any of the extra structures we get after tensor with Fontain's rings. |
Aug 3 |
revised |
Torelli-like theorem for K3 surfaces on terms of its étale cohomology
added 7 characters in body |
Aug 3 |
asked | Torelli-like theorem for K3 surfaces on terms of its étale cohomology |