Related papers: J-holomorphic curves in a nef class

The paper gives topological as well as rigid isotopy classification of smooth irreducible algebraic curves in the real projective 3-space for the case when the degree of the curve is at most six and its genus is at most one.

In this paper, we prove that: For any given finitely many distinct points $P_1,...,P_r$ and a closed subvariety $S$ of codimension $\geq 2$ in a complete toric variety over a uncountable (characteristic 0) algebraically closed field, there…

We investigate N\'eron models of Jacobians of singular curves over strictly Henselian discretely valued fields, and their behaviour under tame base change. For a semiabelian variety, this behaviour is governed by a finite sequence of (a…

We consider flat families of reduced curves on a smooth surface S such that each member C has the same number of singularities of fixed singularity types and the corresponding (locally closed) subscheme H of the Hilbert scheme of S. We are…

We study the compactness problem for moduli spaces of holomorphic supercurves which, being motivated by supergeometry, are perturbed such as to allow for transversality. We give an explicit construction of limiting objects for sequences of…

A viable and still unproved conjecture states that, if $X$ is a smooth algebraic surface and $C$ is a smooth algebraic curve in $X$, then $C$ realizes the smallest possible genus amongst all smoothly embedded $2$-manifolds in its homology…

We introduce a new link invariant called the algebraic genus, which gives an upper bound for the topological slice genus of links. In fact, the algebraic genus is an upper bound for another version of the slice genus proposed here: the…

We determine all genus 2 curves, defined over $\mathbb C$, which have simultaneously degree 2 and 3 elliptic subcovers. The locus of such curves has three irreducible 1-dimensional genus zero components in $\mathcal M_2$. For each component…

The Heegaard genus g of an irreducible closed orientable 3-manifold puts a limit on the number and complexity of the pieces that arise in the Jaco-Shalen-Johannson decomposition of the manifold by its canonical tori. For example, if p of…

The purpose of this paper is to list the refined Humbert invariants for a given automorphism group of a curve $C/K$ of genus 2 over an algebraically closed field $K$ with characteristic $0$. This invariant is an algebraic generalization of…

We denote by $\mathcal{H}_{d,g,r}$ the Hilbert scheme of smooth curves, which is the union of components whose general point corresponds to a smooth, irreducible and non-degenerate curve of degree $d$ and genus $g$ in $\mathbb{P}^r.$ In…

We prove that the cohomology class of any curve on a very general principally polarized abelian variety of dimension at least 4 is an even multiple of the minimal class. The same holds for the intermediate Jacobian of a very general cubic…

Normal forms of almost complex structures in a neighborhood of pseudoholomorphic curve are considered. We define normal bundles of such curves and study the properties of linear bundle almost complex structures. We describe 1-jet of the…

We find that non-hyperelliptic generalised Howe curves and their twists of genus 5 attain the Hasse-Weil-Serre bound over some finite fields of order p, p^2 or p^3 for a prime p. We are able to decompose their Jacobians completely under…

This article is devoted to studying complex algebraic sets under (global) blow-spherical equivalence. The main results of this article are complete classifications of complex algebraic curves. Firstly, we present a complete classification…

In this paper we show that a smooth toric variety $X$ of Picard number $r\leq 3$ always admits a nef primitive collection supported on a hyperplane admitting non-trivial intersection with the cone $\Nef(X)$ of numerically effective divisors…

The category of exploded torus fibrations is an extension of the category of smooth manifolds in which some adiabatic limits look smooth. (For example, the limits considered in tropical geometry appear smooth, also degenerations…

We study the Hilbert scheme $\mathcal{H}^\mathcal{L}_{d,g,r}$ parametrizing smooth, irreducible, non-degenerate and linearly normal curves of degree $d$ and genus $g$ in $\mathbb{P}^r$ whose complete and very ample hyperplane linear series…

Let $X$ be a projective variety with log terminal singularities and vanishing augmented irregularity. In this paper we prove that if $X$ admits a relatively minimal genus one fibration then it does contain a subvariety of codimension one…

This article is concerned with the question of whether an energy bound implies a genus bound for pseudo-holomorphic curves in almost complex manifolds. After reviewing what is known in dimensions other than 6, we establish a new result in…