8,922 research outputs found
Q_l-cohomology projective planes and singular Enriques surfaces in characteristic two
We classify singular Enriques surfaces in characteristic two supporting a
rank nine configuration of smooth rational curves. They come in one-dimensional
families defined over the prime field, paralleling the situation in other
characteristics, but featuring novel aspects. Contracting the given rational
curves, one can derive algebraic surfaces with isolated ADE-singularities and
trivial canonical bundle whose Q_l-cohomology equals that of a projective
plane. Similar existence results are developed for classical Enriques surfaces.
We also work out an application to integral models of Enriques surfaces (and K3
surfaces).Comment: 24 pages; v3: journal version, correcting 20 root types to 19 and
ruling out the remaining type 4A_2+A_1 (in new section 11
Q`-cohomology projective planes and Enriques surfaces in characteristic two
We classify singular Enriques surfaces in characteristic two supporting a rank nine configuration of smooth rational curves. They come in one-dimensional families defined over the prime field, paralleling the situation in other characteristics, but featuring novel aspects. Contracting the given rational curves, one can derive algebraic surfaces with isolated ADE-singularities and trivial canonical bundle whose Q`-cohomology equals that of a projective plane. Similar existence results are developed for classical Enriques surfaces. We also work out an application to integral models of Enriques surfaces (and K3 surfaces)
Picard groups on moduli of K3 surfaces with Mukai models
We discuss the Picard group of moduli space of
quasi-polarized K3 surfaces of genus and . In this range,
is unirational and a general element in is a
complete intersection with respect to a vector bundle on a homogenous space, by
the work of Mukai. In this paper, we find generators of the Picard group
using Noether-Lefschetz theory. This verifies
the Noether-Lefschetz conjecture on moduli of K3 surfaces in these cases.Comment: fix some typo
Mirror symmetry, Tyurin degenerations and fibrations on Calabi-Yau manifolds
We investigate a potential relationship between mirror symmetry for
Calabi-Yau manifolds and the mirror duality between quasi-Fano varieties and
Landau-Ginzburg models. More precisely, we show that if a Calabi-Yau admits a
so-called Tyurin degeneration to a union of two Fano varieties, then one should
be able to construct a mirror to that Calabi-Yau by gluing together the
Landau-Ginzburg models of those two Fano varieties. We provide evidence for
this correspondence in a number of different settings, including
Batyrev-Borisov mirror symmetry for K3 surfaces and Calabi-Yau threefolds,
Dolgachev-Nikulin mirror symmetry for K3 surfaces, and an explicit family of
threefolds that are not realized as complete intersections in toric varieties.Comment: v2: Section 5 has been completely rewritten to accommodate results
removed from Section 5 of arxiv:1501.04019. v3: Final version, to appear in
String-Math 2015, forthcoming volume in the Proceedings of Symposia in Pure
Mathematics serie
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