Related papers: Involutions on hyperelliptic curves and Prym maps
We get new results (and rederive some know ones) on smooth surfaces in $\mathbb{R}^n$ by unifying several view points into a coherent general view. Namely, we show and use new relations of the evolute (caustic) with the curvature ellipse,…
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 $E$…
The orientability problem in real Gromov-Witten theory is one of the fundamental hurdles to enumerating real curves. In this paper, we describe topological conditions on the target manifold which ensure that the uncompactified moduli spaces…
Embedding diagrams have been used extensively to visualize the properties of curved space in Relativity. We introduce a new kind of embedding diagram based on the {\it extrinsic} curvature (instead of the intrinsic curvature). Such an…
We explore the concept of projections of syzygies and prove two new technical results; we firstly give a precise characterization of syzygy schemes in terms of their projections, secondly, we prove a converse to Aprodu's Projection Theorem.…
The first part of this note contains a review of basic properties of the variety of lines contained in an embedded projective variety and passing through a general point. In particular we provide a detailed proof that for varieties defined…
We study one-parameter curves on the universal Teichm\"uller space $T$ and on the homogeneous space $M=\Diff S^1/\Rot S^1$ embedded into $T$. As a result, we deduce evolution equations for conformal maps that admit quasiconformal extensions…
In a previous paper, the authors proved that the Prym variety of any non-cyclic etale triple cover of a smooth curve of genus 2 is a Jacobian variety of dimension 2. This gives a map from the moduli space of such covers to the moduli space…
By a theorem of Wahl, the canonically embedded curves which are hyperplane section of K3 surfaces are distinguished by the non-surjectivity of their Wahl map. In this paper we address the problem of distinguishing hyperplane sections of…
We study infinite superelliptic curves as translation surfaces and explore their Veech groups. These objects are branched covering of the complex plane with branching over infinitely many points. We provide a criterion for isomorphism…
Let $k$ be a field of characteristic zero containing a primitive $n$-th root of unity. Let $C^0_n$ be a singular plane curve of degree $n$ over $k$ admitting an order $n$ automorphism, $n$ nodes as the singularities, and $C_n$ be its…
This note contains an elementary discussion of the Arakelov intersection theory of elliptic curves. The main new results are a projection formula for elliptic arithmetic surfaces and a formula for the "energy" of an isogeny between Riemann…
In 2014 A. Degtyarev, I. Itenberg and the author gave a description, up to fiberwise equivariant deformations, of maximally inflected real trigonal curves of type~I (over a base $ B $ of an arbitrary genus) in terms of the combinatorics of…
The arrangement of all Galois lines for the quotient curve of the Hermitian curve by an involution in the projective 3-space is described, in terms of the geometry over finite fields. All Galois points for three plane models of this curve…
Homology of braid groups and Artin groups can be related to the study of spaces of curves. We completely calculate the integral homology of the family of smooth curves of genus $g$ with one boundary component, that are double coverings of…
Rafi and Schleimer recently proved that the natural relation between curve complexes induced by a covering map between two surfaces is a quasi-isometric embedding. We offer another proof of this result using a distance estimate via…
We develop a theory of Prym varieties and cubic threefolds over fields of characteristic $2$. As an application, we prove that smooth cubic threefolds are non-rational over an arbitrary field and solve a conjecture of Deligne regarding…
This article is about the graph genus of certain well studied graphs in surface theory: the curve, pants and flip graphs. We study both the genus of these graphs and the genus of their quotients by the mapping class group. The full graphs,…
In this paper, we consider the intensity surface of a 2D image, we study the evolution of the symmetry sets (and medial axes) of 1-parameter families of iso-intensity curves. This extends the investigation done on 1-parameter families of…
On a closed symplectic surface Sigma of genus two or more, we give a new construction of an extended flux map (a crossed homomorphism from the symplectomorphism group Symp(Sigma) to the cohomology group H^1(Sigma;R) that extends the flux…