Related papers: Cyclic Covers over Strongly Liftable Schemes

Given a smooth affine curve X over a field k of positive characteristic, and an overconvergent F-isocrystal on X, we prove after replacing k by a finite purely inseparable extension, there exists a finite separable cover of X, the pullback…

The circular coordinates algorithm, a key tool in topological data analysis, relies on a theoretically unvalidated lifting step to convert cocycles from a prime field to integer coefficients. We provide a rigorous analysis of this…

Very ampleness criteria for rank 2 vector bundles over smooth, ruled surfaces over rational and elliptic curves are given. The criteria are then used to settle open existence questions for some special threefolds of low degree.

We consider the question whether a real threefold X fibred into quadric surfaces over the real projective line is stably rational (over R) if the topological space X(R) is connected. We give a counterexample. When all geometric fibres are…

Esnault-Viehweg developed the theory of cyclic branched coverings $\tilde X\to X$ of smooth surfaces providing a very explicit formula for the decomposition of $H^1(\tilde X,\mathbb{C})$ in terms of a resolution of the ramification locus.…

We find a criterion for an effective divisor $D$ on a smooth surface to be left-orthogonal or strongly left-orthogonal (i.e. for the pair of line bundles $(\mathcal O,\mathcal O(D))$ to be exceptional or strong exceptional).

We obtain a complete list of smooth projective threefolds over $\mathbb C$ for which the dimension of the space of vanishing cycles (in $H^2$ of the smooth hyperplane section) equals $2$. We also obtain a complete list of rank 2 very ample…

We study effective divisors $D$ on surfaces with $H^0(\mathcal O_D)=k$ and $H^1(\mathcal O_D)=H^0(\mathcal O_D(D))=0$. We give a numerical criterion for such divisors, following a general investigation of negativity, rigidity and…

Ballico proved that a smooth projective variety $X$ of degree $d$ over a finite field of $q$ elements admits a smooth hyperplane section if $q\geq d(d-1)^{\dim X}$. In this paper, we refine this criterion for higher codimensional linear…

We prove that every proper subspace of the moduli space of stable surfaces with fixed volume over an algebraically closed field of characteristic p>5 is projective. As a consequence we also deduce that the same moduli space is projective…

For any prime $p>0$, we prove that simple superspecial abelian surfaces over $\mathbb{F}_{p}$ admit CM liftings after base change at most to $\mathbb{F}_{p^2}$, by using the residual reflex condition (RRC) and Lie types. The CM-liftability…

A fake quadric is a smooth projective surface that has the same rational cohomology as a smooth quadric surface but is not biholomorphic to one. We provide an explicit classification of all irreducible fake quadrics according to the…

We establish the slope equality and give an upper bound of the slope for finite cyclic covering fibrations of an elliptic surface including bielliptic fibrations of genus greater than 5. We also give an upper bound of the slope for triple…

The purpose of this paper is to investigate the properties of spectral and tiling subsets of cyclic groups, with an eye towards the spectral set conjecture in one dimension, which states that a bounded measurable subset of $\mathbb{R}$…

In this paper, we find criteria for when cyclic cubic and cyclic quartic fields have well-rounded ideal lattices. We show that every cyclic cubic field has at least one well-rounded ideal. We also prove that there exist families of cyclic…

We show that any hyperplane section of a variety which is the inverse image of a smooth variety of dimension at least 2 by an endomorphism (wich is not an automorphism) of the projective space, is linearly complete. We stress the case of…

We show that the residual categories of quadric surface bundles are equivalent to the (twisted) derived categories of some scheme under the following hypotheses. Case 1: The quadric surface bundle has a smooth section. Case 2: The total…

Efficient representations of convex sets are of crucial importance for many algorithms that work with them. It is well-known that sometimes, a complicated convex set can be expressed as the projection of a much simpler set in higher…

We compute explicit bases for the de Rham cohomology of cyclic covers of the projective line defined over an algebraically closed field of characteristic $p\geq 0$. For both Kummer and Artin-Schreier extensions, we describe precise…

We prove a sufficient condition for a finite clique complex to collapse to a $k$-dimensional complex, and use this to exhibit thresholds for $(k+1)$-collapsibility in a sparse random clique complex. In particular, if every strongly…