Related papers: On the constellations of Weierstrass points

Let $N$ be a connected nonorientable surface of genus $g$ with $n$ punctures. Suppose that $g$ is odd and $g+n \geqslant 6$. We prove that the automorphism group of the complex of curves of $N$ is isomorphic to the mapping class group…

We present an explicit construction of a compactification of the locus of smooth curves whose symmetric Weierstrass semigroup at a marked point is odd. The construction is an extension of Stoehr's techniques using Pinkham'sequivariant…

We prove that, if two germs of plane curves $(C,0)$ and $(C',0)$ with at least one singular branch are equivalent by a (real) smooth diffeomorphism, then $C$ is complex isomorphic to $C'$ or to $\overline{C'}$. A similar result was shown by…

Consider a hyperelliptic curve of genus $2$ over a field $K$ of characteristic zero. After extending $K$ we can view it as a marked curve with its $6$ Weierstrass points. We classify the structure of the potentially stable reduction of such…

We show that all GL(2, R)-equivariant point markings over orbit closures of primitive genus two translation surfaces arise from marking pairs of points exchanged by the hyperelliptic involution, Weierstrass points, or the golden points in…

The combination of this paper and its companion complete the classification of monodromy groups of indecomposable coverings of complex curves $f:X\rightarrow \mathbb P^1$ of sufficiently large degree in comparison to the genus of $X$. In…

We describe the ring of modular forms of degree 2 in characteristic 2 using its relation with curves of genus 2.

Using meromorphic differentials with real periods, we prove Arbarello's conjecture: any compact complex cycle of dimension $g-n$ in the moduli space $\M_g$ of smooth genus $g$ algebraic curves must intersect the locus of curves having a…

We settle the automorphism groups of curves appearing in a classification list of smooth plane curves with at least two Galois points. One of them is an ordinary curve whose automorphism group exceeds the Hurwitz bound.

We show that for any elliptic curve (with j invariant not 0 or 1728) over any field of characteristic different from 2 and 3, there exists an hyperelliptic curve H of genus 5 with two independent maps to the given elliptic curve. We also…

For conic bundles on a smooth variety (over a field of characteristic $\ne 2$) which degenerate into pairs of distinct lines over geometric points of a smooth divisor, we prove a theorem which relates the Brauer class of the non-degenerate…

By analogy with the classical (Chasles-Schubert-Semple-Tyrell) spaces of complete quadrics and complete collineations, we introduce the variety of complete complexes. Its points can be seen as equivalence classes of spectral sequences of a…

We study the minimal Weierstrass equations for genus 2 curves defined over a ring of integers $\mathcal O_{\mathbb F}$. This is done via reduction theory and Julia invariant of binary sextics. We show that when the binary sextics has extra…

We show that on a metric graph of genus $g$, a divisor of degree $n$ generically has $g(n-g+1)$ Weierstrass points. For a sequence of generic divisors on a metric graph whose degrees grow to infinity, we show that the associated Weierstrass…

In this article we use techniques from coding theory to derive upper bounds for the number of rational places of the function field of an algebraic curve defined over a finite field. The used techniques yield upper bounds if the…

Let C be the union of two general connected, smooth, nonrational curves X and Y intersecting transversally at a point P. Assume that P is a general point of X or of Y. Our main result, in a simplified way, says: Let Q be a point of X. Then…

The aim of this paper is to review the main techniques in the computation of Weierstra\ss semigroup at several points of curves defined over perfect fields, with special emphasis on the case of two points. Some hints about the usage of some…

Consider the elliptic curve $E$ given by the Weierstrass equation $y^2 = x^3 - 11x - 14$, which has complex multiplication by the order of conductor $2$ inside $\mathbb{Z}[i]$. It was recently observed in a paper of Daniels and…

In this paper we demonstrate that the notion of inflection points and extactic points on plane algebraic curves can be suitably transferred to curves in $\mathbb{P}^1\times \mathbb{P}^1$. More precisely, we describe osculating curves and…

Let $X$ (resp. $Y$) be a curve of genus 1 (resp. 2) over a base field $k$ whose characteristic does not equal 2. We give criteria for the existence of a curve $Z$ over $k$ whose Jacobian is up to twist (2,2,2)-isogenous to the products of…