Brave new local moduli for ordinary K3 surfaces
نویسنده
چکیده
It is shown that the K3 spectra which refine the local rings of the moduli stack of ordinary p-primitively polarized K3 surfaces in characteristic p allow for an E∞ structure which is unique up to equivalence. This uses the E∞ obstruction theory of Goerss and Hopkins and the description of the deformation theory of such K3 surfaces in terms of their Hodge F-crystals due to Deligne and Illusie. Furthermore, all automorphism of such K3 surfaces can be realized by E∞ maps which are unique up to homotopy, and this can by rigidified to an action if the automorphism group is tame. MSC 2000: 14F30, 14J28, 55N22, 55P43, 55S12, 55S25.
منابع مشابه
Crystals and derived local moduli for ordinary K3 surfaces
It is shown that the K3 spectra which refine the local rings of the moduli stack of ordinary p-primitively polarized K3 surfaces in characteristic p allow for an E∞ structure which is unique up to equivalence. This uses the E∞ obstruction theory of Goerss and Hopkins and the description of the deformation theory of such K3 surfaces in terms of their Hodge F-crystals due to Deligne and Illusie. ...
متن کاملK 3 spectra Markus
We introduce the notion of a K3 spectrum in analogy with that of an elliptic spectrum and show that there are “enough” K3 spectra in the sense that for all K3 surfaces X in a suitable moduli stack of K3 surfaces there is a K3 spectrum whose underlying ring is isomorphic to the local ring of the moduli stack in X with respect to the etale topology, and similarly for the ring of formal functions ...
متن کاملThe rationality of the moduli spaces of Coble surfaces and of nodal Enriques surfaces
The purpose of this note is to prove the rationality of the moduli spaces of Coble surfaces and of nodal Enriques surfaces over the field of complex numbers. A Coble surface is a rational surface obtained by blowing up 10 nodes of a rational plane curve of degree 6, and an Enriques surface is said to be nodal if it contains a smooth rational curve. The moduli space of nodal Enriques surfaces is...
متن کاملN-Point Deformation of Algebraic K3 Surfaces
We consider N-point deformation of algebraic K3 surfaces. First, we construct two-point deformation of algebraic K3 surfaces by considering algebraic deformation of a pair of commutative algebraic K3 surfaces. In this case, the moduli space of the noncommutative deformations is of dimension 19, the same as the moduli dimension of the complex deformations of commutative algebraic K3 surfaces. Th...
متن کاملInstanton Moduli as a Novel Map from Tori to K3-surfaces
A map is constructed from the moduli of hyper-KK ahler tori to hyper-KK ahler K3 surfaces which does not coincide with the Kummer map. The map takes a torus to the moduli space of SO(3) connections on a bundle with nontrivial rst Stiefel-Whitney class and rst Pontrjagin class equal to-4. This map is shown to intersect the Kummer moduli and also certain subvarieties of singular K3 surfaces. Our ...
متن کامل