Related papers: Cyclic Covers over Strongly Liftable Schemes
We study slope stability of smooth surfaces and its connection with exceptional divisors. We show that a surface containing an exceptional divisor with arithmetic genus at least two is slope unstable for some polarisation. In the converse…
We prove that for any field k of characteristic p>0, any separated scheme X of finite type over k, and any overconvergent F-isocrystal E over X, the rigid cohomology H^i(X, E) and rigid cohomology with compact supports H^i_c(X,E) are finite…
Supercyclides are surfaces with a characteristic conjugate parametrization consisting of two families of conics. Patches of supercyclides can be adapted to a Q-net (a discrete quadrilateral net with planar faces) such that neighboring…
We introduce an elementary transformation called flips on tilings by squares and triangles and conjecture that it connects any two tilings of the same region of the Euclidean plane.
We study soft supersymmetry breaking terms for anisotropic LARGE volume compactifications, where the bulk volume is set by a fibration with one small four-cycle and one large two-cycle. We consider scenarios where D7s wrap either a blow-up…
Cyclic coverings produce many examples of topologically contractible smooth affine complex varieties. In this paper, we study the motivic cohomology groups of cyclic coverings over algebraically closed fields of characteristic $0$. In…
A characterization of a class of optimal three-weight cyclic codes of dimension 3 over any finite field was recently presented in [10]. Shortly after this, a generalization for the sufficient numerical conditions of such characterization…
An isomorphism of symplectically tame smooth pseudocomplex structures on the complex projective plane which is a homeomorphism and differentiable of full rank at two points is smooth.
Given a connected smooth projective surface X over the complex numbers, together with a simple normal crossings divisor D on it, we study finite normal covers Y of X that are unramified outside D. Given moreover a fibration of X onto a…
Given a compact, oriented surface $S$ of finite genus and finitely many boundary components, we provide examples of finite covers $\tilde{S}$ of $S$ and non-simple closed curves $\gamma$ on $S$ which lifts to simple closed curves on…
Let $p$ be an odd prime. Let $K/\mathbb{Q}_p$ be a finite unramified extension. Let $\rho: G_K \to GL_2(\overline{\mathbb{F}}_p)$ be a continuous representation. We prove that $\rho$ has a crystalline lift of small irregular weight if and…
Let $f:S\to B$ be a finite cyclic covering fibration of a fibered surface. We study the lower bound of slope $\lambda_{f}$ when the relative irregularity $q_{f}$ is positive.
Relations between some kinds of formal and standard smoothness, for morphisms of schemes, are clarified in surprisingly simple and direct ways, bypassing much of the customarily employed machinery. Even the deep local-to-global property of…
We construct k-parameter families of rational surface automorphisms for any k. These are automorphisms of surfaces X, which are constructed from iterated blowups over the projective plane. In certain cases: we are able to determine the…
We give two "lifting" constructions of strongly regular Cayley graphs. In the first construction we "lift" a cyclotomic strongly regular graph by using a subdifference set of the Singer difference set. The second construction uses quadratic…
We give examples of smooth plane quartics over $\mathbb{Q}$ with complex multiplication over $\overline{\mathbb{Q}}$ by a maximal order with primitive CM type. We describe the required algorithms as we go, these involve the reduction of…
A digraph $G$ is weightable if its edges can be weighted with real numbers such that the total weight in each directed cycle equals 1. There are several equivalent conditions: that $G$ admits a 0/1-weighting with the same property, or that…
Let X be a smooth, complete, toric variety. We study those curves C in X that are contractible, in the sense that there exists an equivariant morphism with connected fibers, with source X, that contracts exactly the irreducible curves that…
We give a $K$-theoretic criterion for a quasi-projective variety to be smooth. If $\mathbb{L}$ is a line bundle corresponding to an ample invertible sheaf on $X$, it suffices that $K_q(X) = K_q(\mathbb{L})$ for all $q\le\dim(X)+1$.
We provide the main results of a deformation theory of smooth formal schemes. First we deal with the case of global lifting of smooth morphisms. We prove that the obstruction to the existence of a global lifting lies in a Ext^1 group. Then…