Related papers: Non-special scrolls with general moduli
A theory of graded manifolds can be viewed as a generalization of differential geometry of smooth manifolds. It allows one to work with functions which locally depend not only on ordinary real variables, but also on $\mathbb{Z}$-graded…
We study the Drinfeld modular curves arising from the Hecke congruence subgroups of $\mathrm{SL}_2(\mathbb{F}_q[T])$. Using a combinatorial method of Gekeler and Nonnengardt, we obtain a genus formula for these curves. In cases when the…
This is the revised version of our previous preprint. In this paper, we establish a generic smoothness result for moduli space of semistable sheaves of arbitrary rank over surfaces provided that the second Chern class of the sheaves is…
We consider the moduli space of genus 4 curves endowed with a $g^1_3$ (which maps with degree 2 onto the moduli space of genus 4 curves). We prove that it defines a degree $\frac{1}{2}(3^{10}-1)$ cover of the 9-dimensional Deligne-Mostow…
New families of algebras and DG algebras with two simple modules are introduced and described. Using the twisted tensor product operation, we prove that such algebras have finite global dimension, and the resulting DG algebras are smooth.…
In this paper we give a precise classification of the pairs $(C,\widetilde{B})$ with $C$ a smooth curve of genus $g$ and $\widetilde{B}\subset C^{(2)}$ a curve of degree two and positive self-intersection. We prove that there are no such…
In this article we consider moduli properties of singular curves on K3 surfaces. Let $\mathcal{B}_g$ denote the stack of primitively polarized K3 surfaces $(X,L)$ of genus $g$ and let $\mathcal{T}^n_{g,k} \to \mathcal{B}_g$ be the stack…
Let $X$ be a nonsingular projective surface over an algebraically closed field with characteristic zero, and $H_-$ and $H_+$ ample line bundles on $X$ separated by only one wall of type $(c_1,c_2)$. Suppose the moduli scheme $M(H_-)$ of…
We study surfaces of general type $S$ whose cotangent sheaf is generated by its global sections. We define a map called the cotangent map of $S$ that enables us to understand the obstructions to the ampleness of the cotangent sheaf of $S$.…
Severi varieties and Brill-Noether theory of curves on K3 surfaces are well understood. Yet, quite little is known for curves on abelian surfaces. Given a general abelian surface $S$ with polarization $L$ of type $(1,n)$, we prove…
The aim of this paper is the computation of the degree and genus of all incidence scrolls in Pn. For this, we fix the dimension of a linear space which have a base space of this fixed dimension. In this way, we can obtain all the incidence…
We study stable curves of arithmetic genus 2 which admit two morphisms of finite degree $p$, resp. $d$, onto smooth elliptic curves, with particular attention to the case $p$ prime.
We study the variation of linear sections of hypersurfaces in $\mathbb{P}^n$. We completely classify all plane curves, necessarily singular, whose line sections do not vary maximally in moduli. In higher dimensions, we prove that the family…
We study non-commutative projective lines over not necessarily algebraic bimodules. In particular, we give a complete description of their categories of coherent sheaves and show they are derived equivalent to certain bimodule species. This…
In this paper, we investigate the differential smoothness of graded skew Clifford algebras.
We study the gonality and canonical model of a rational unicuspidal curve C. We are mainly interested in the case where C is non-Gorenstein. We classify such curves via different notions of gonality, and by its canonical model C', up to…
Consider genus $g$ curves that admit degree $d$ covers to elliptic curves only branched at one point with a fixed ramification type. The locus of such covers forms a one parameter family $Y$ that naturally maps into the moduli space of…
The paper considers the extension of the T-spline approach to the Generalized B-splines (GB-splines), a relevant class of non-polynomial splines. The Generalized T-splines (GT-splines) are based both on the framework of classical polynomial…
In this note, we describe the possible singularities on a stable surface which is in the boundary of the moduli space of surfaces isogenous to a product. Then we use the $\mathbb Q$-Gorenstein deformation theory to get some connected…
In this article we investigate the algebra and geometry of dihedral covers of smooth algebraic varieties. To this aim we first describe the Weil divisors and the Picard group of divisorial sheaves on normal double covers. Then we provide a…