Related papers: Covers of Elliptic Curves with Unique, Totally Ram…
In this paper, we investigate the possibility of constructing isomonodromic deformations of logarithmic connections on curves by using ramified covers. We give new examples and prove a classification result.
In this paper, we first summarize the existing algorithms for computing all the generalized asymptotes of a plane algebraic curve implicitly or parametrically defined. From these previous results, we derive a method that allows to easily…
In this article, we construct algebraic equations for a curve C and a map f to an elliptic curve E, with pre-specified branching data. We do this by determining certain relations that the periods of C and E must satisfy and use these…
Consider genus g curves that admit degree d covers to an elliptic curve simply branched at 2g-2 points. Vary a branch point and the locus of such covers forms a one-parameter family W. We investigate the geometry of W by using admissible…
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 topology of symplectic 4-manifolds is related to that of singular plane curves via the concept of branched covers. Thus, various classification problems concerning symplectic 4-manifolds can be reformulated as questions about singular…
The embeddings of complex plane projective curves in the plane are a cornerstone of the topological study of algebraic varieties. In this work, we deal with the local and global aspects of these embeddings, with a special attention to its…
We give the complete list of possible torsion subgroups of elliptic curves with complex multiplication over number fields of degree 1-13. Additionally we describe the algorithm used to compute these torsion subgroups and its implementation.
We consider the problem of checking whether an elliptic curve defined over a given number field has complex multiplication. We study two polynomial time algorithms for this problem, one randomized and the other deterministic. The randomized…
In this note, we introduce the notion of an unramified strongly cyclic covering for a cyclic curve, a class that has similar properties to, and contains, unramified double covers of hyperelliptic curves. We determine several of their basic…
In this paper, we study the computation of curvatures at the singular points of algebraic curves and surfaces. The idea is to convert the problem to compute the curvatures of the corresponding regular parametric curves and surfaces, which…
This is the paper as published. The topology of a complex plane curve singularity with real branches is deduced from any real deformation having delta crossings. An example of the computation of the global geometric monodromy of a…
We prove that each counting function of the m-simple branched covers with a fixed genus of an elliptic curve is expressed as a polynomial of the Eisenstein series E_2, E_4 and E_6 . The special case m=2 is considered by Dijkgraaf.
In this article, we compute the braid monodromy of two algebraic curves defined over R. These two curves are of complex level not bigger than 6, and they are unions of lines and conics. We use two different techniques for computing their…
Enumerative algebraic geometry deals with problems of counting geometric objects defined algebraically, An important class of enumerative problems is that of counting curves: given a class of curves in some projective variety defined by…
Elliptic curves over finite fields with predefined conditions in the order are practically constructed using the theory of complex multiplication. The stage with longest calculations in this method reconstructs some polynomial with integer…
Braid monodromy is an important tool for computing invariants of curves and surfaces. In this paper, the \emph{rectangular braid diagram (RBD)} method is proposed to compute the braid monodromy of a completely reducible $n$-gonal curve,…
We propose an algebraic method for the classification of branched Galois covers of a curve $X$ focused on studying Galois ring extensions of its geometric adele ring $\A_{X}$. As an application, we deal with cyclic covers; namely, we…
The arithmetic of elliptic curves, namely polynomial addition and scalar multiplication, can be described in terms of global sections of line bundles on $E\times E$ and $E$, respectively, with respect to a given projective embedding of $E$…
There are many numerical methods for solving partial different equations (PDEs) on manifolds such as classical implicit, finite difference, finite element, and isogeometric analysis methods which aim at improving the interoperability…