Related papers: Embedding pointed curves in K3 surfaces

We consider coverings of real algebraic curves to real rational algebraic curves. We show the existence of such coverings having prescribed topological degree on the real locus. From those existence results we prove some results on…

This article classifies Knutsen K3 surfaces all of whose hyperplane sections are irreducible and reduced. As an application, this gives infinite families of K3 surfaces of Picard number two whose general hyperplane sections are…

We give new relations between geometric invariants of $K3$ surfaces with purely non-symplectic automorphisms of order 4 and 6. Our approach is based on a comparison of two methods of computation of formulas for the Euler characteristic of…

Under natural hypotheses we give an upper bound on the dimension of families of singular curves with hyperelliptic normalizations on a surface S with p_g(S) >0 via the study of the associated families of rational curves in Hilb^2(S). We use…

The geometric objects of study in this paper are K3 surfaces which admit a polarization by the unique even unimodular lattice of signature (1,17). A standard Hodge-theoretic observation about this special class of K3 surfaces is that their…

Patchworking theorems serve as a basic element of the correspondence between tropical and algebraic curves, which is a core of the tropical enumerative geometry. We present a new version of a patchworking theorem which relates plane…

The aim of this paper is to classify mildly singular Calabi-Yau threefolds fibred in low-degree weighted K3 surfaces and embedded as anticanonical hypersurfaces in weighted scrolls, extending results of Mullet. We also study projective…

We describe the possible 3-divisible $A_2^n$ configurations of smooth rational curves on K3 surfaces in characteristic 3 and fully classify the resulting triple covers.

We give a simple proof of the statement that every rational curve in the primitive class of a general K3 surface is nodal.

We consider K3 surfaces of Picard rank 14 which admit a purely nonsymplectic automorphism of order 16. The automorphism acts on the second cohomology group with integer coefficients and we compute the invariant sublattice for the action. We…

In this note we present the classification of non-symplectic automorphisms of prime order on K3 surfaces, i.e.we describe the topological structure of their fixed locus and determine the invariant lattice in cohomology. We provide new…

We pose the problem to determine explicit defining equations of various elliptic fibrations on a given $K3$ surface, and study the case of the Kummer surfaces of the product of two elliptic curves.

In this paper we compute the gonality and the dimension of the Brill-Noether loci $W^1_d(C)$ for curves in a non primitive linear system of a simple abelian surface, adapting vector bundles techniques \`a la Lazarsfeld originally introduced…

We show that if over some number field there exists a certain diagonal plane cubic curve that is locally solvable everywhere, but that does not have points over any cubic galois extension of the number field, then the algebraic part of the…

We describe a method to show that certain elliptic surfaces do not admit purely inseparable multisections (equivalently, that genus one curves over function fields admit no points over the perfect closure of the base field) and use it to…

Using a construction of Hassett--V\'arilly-Alvarado, we produce derived equivalent twisted K3 surfaces over $\mathbb{Q}$, $\mathbb{Q}_2$, and $\mathbb{R}$, where one has a rational point and the other does not. This answers negatively a…

We prove that the gonality among the smooth curves in a complete linear system on a $K3$ surface is constant except for the Donagi-Morrison example. This was proved by Ciliberto and Pareschi under the additional condition that the linear…

We answer some enumerative questions about irreducible rational curves on Hirzebruch surfaces, by combining an idea of Kontsevich with the study of the geometry of certain natural parameter spaces. Our formulas generalize Kontsevich's…

In this note, we report some progress we made recently on the automorphisms groups of K3 surfaces. A short and straightforward proof of the impossibility of Z/(60) acting purely non-symplectically on a K3 surface, is also given, by using…

A K3 surface is a quaternionic analogue of an elliptic curve from a view point of moduli of vector bundles. We can prove the algebraicity of certain Hodge cycles and a rigidity of curve of genus eleven and gives two kind of descriptions of…