Related papers: Strongly Cyclic Coverings of Cyclic Curves
Elliptic curves have a well-known and explicit theory for the construction and application of endomorphisms, which can be applied to improve performance in scalar multiplication. Recent work has extended these techniques to hyperelliptic…
The categories with noninvertible morphisms are studied analogously to the semisupermanifolds with noninvertible transition functions. The concepts of regular n-cycles, obstruction and the regularization procedure are introduced and…
For a finite group $G$, let $\H_{g,G,\xi}$ be the stack of admissible $G$-covers $C\to D$ of stable curves with ramification data $\xi$, $g(C)=g$ and $g(D)=g'$. There are source and target morphisms $\phi\colon \H_{g,G,\xi}\to \M_{g,r}$ and…
By considering appropriate finite covering spaces of closed non-orientable surfaces, we construct linear representations of their mapping class group which have finite index image in certain big arithmetic groups.
In this paper we introduce an algorithm of construction of cyclic space-filling curves. One particular construction provides a family of space-filling curves in all dimensions (H-curves). They are compared here with the Hilbert curve in the…
We prove the existence of canonical scrolls; that is, scrolls playing the role of canonical curves. First of all, they provide the geometrical version of Riemann Roch Teorem: any special scroll is the projection of a canonical scroll and…
Conics and Cartesian ovals are very important curves in various fields of science. Also aspheric curves based on conics are useful in optics. Superconic curves recently suggested by A. Greynolds are extensions of both conics and Cartesian…
The Prym variety for a branched double covering of a nonsingular projective curve is defined as a polarized abelian variety. We prove that any double covering of an elliptic curve which has more than $4$ branch points is recovered from its…
We introduce a new logarithmic structure on the moduli stack of stable curves, admitting logarithmic gluing maps. Using this we define cohomological field theories taking values in the logarithmic Chow cohomology ring, a refinement of the…
We study those Lagrangian surfaces in complex Euclidean space which are foliated by circles or by straight lines. The former, which we call cyclic, come in three types, each one being described by means of, respectively, a planar curve, a…
We show that a compact Kahler manifold admitting a nondegenerate holomorphic 2-form valued in a line bundle is a finite cyclic cover of a hyperkahler manifold. With respect to the connection induced by the locally hyperkahler metric, the…
We introduce new obstructions to rationality for geometrically rational threefolds arising from the geometry of curves and their cycle maps.
We study quotients of quasi-affine schemes by unipotent groups over fields of characteristic 0. To do this, we introduce a notion of stability which allows us to characterize exactly when a principal bundle quotient exists and, together…
This article introduces and studies the tight approximation property, a property of algebraic varieties defined over the function field of a complex or real curve that refines the weak approximation property (and the known cohomological…
Let $k$ be an algebraically closed field of positive characteristic $p>0$ and $C \to {\mathbb P}^1_k$ a $p$-cyclic cover of the projective line ramified in exactly one point. We are interested in the $p$-part of the full automorphism group…
We prove necessary and sufficient conditions for a smooth surface in a 4-manifold X to be pseudoholomorphic with respect to some almost complex structure on X. This provides a systematic approach to the construction of pseudoholomorphic…
Let $X$ be a smooth projective variety over an algebraically closed field $k$ of characteristic $p>0$ of $\dim X\geq 4$ and Picard number $\rho(X)=1$. Suppose that $X$ satisfies $H^i(X,F^{m*}_X(\Omg^j_X)\otimes\Ls^{-1})=0$ for any ample…
In this paper, we investigate special curves on a strong r-helix submanifold in Euclidean n-space E n. Also, we give the important relations between strong r-helix submanifolds and the special curves such as line of curvature, geodesic and…
En appliquant des m\'ethodes d\'evelopp\'ees par Koll\'ar, Voisin, nous-m\^emes, Totaro, nous montrons qu'un rev\^etement cyclique de $\mathbb P_{\mathbb C}^n, n\geq 3$ de degr\'e premier $p$, ramifi\'e le long d'une hypersurface tr\`es…
We use admissible covers to characterize irreducible stable curves that are $(d,h)$-elliptic, that is, that are limits of smooth curves admiting finite maps of degree-$d$ to smooth curves of genus $h\geq 1$.