相关论文: The canonical ring of a 3-connected curve

In this paper we study complete linear series on a hyperelliptic curve $C$ of arithmetic genus $g$. Let $A$ be the unique line bundle on $C$ such that $|A|$ is a $g^1_2$, and let $\mathcal{L}$ be a line bundle on $C$ of degree $d$. Then…

Let G be a connected Lie group, G^d the underlying discrete group, and BG, BG^d their classifying spaces. Let R denote the radical of G. We show that all classes in the image of the canonical map in cohomology H^*(BG,R)->H^*(BG^d,R) are…

We determine an explicit presentation by generators and relations of the cohomology algebra $H^*(\mathbb P^2\setminus C,\mathbb C)$ of the complement to an algebraic curve $C$ in the complex projective plane $\mathbb P^2$, via the study of…

We use hyperbolic geometry to construct simply-connected symplectic or complex manifolds with trivial canonical bundle and with no compatible Kahler structure. We start with the desingularisations of the quadric cone in C^4: the smoothing…

Let $(S,D)$ be a minimal log pair of general type with $S$ a smooth projective surface and $D$ a simple normal corssing reduced divisor on $S$. We assume that its log canonial linear system $|K_S+D|$ is composed of a penciel, let $f\colon…

We prove that a smooth, complex plane curve $C$ of odd degree can be defined by a polynomial with real coefficients if and only if $C$ is isomorphic to its complex conjugate. Counterexamples are known for curves of even degree. More…

Based on a recent result of Voisin [2001] we describe the last nonzero syzygy space in the linear strand of a canonical curve C of even genus g=2k lying on a K3 surface, as the ambient space of a k-2-uple embedded P^{k+1}. Furthermore the…

The paper is a contribution to the conjecture of Kobayashi that the complement of a generic curve in the projective plane is hyperbolic, provided the degree is at least five. Previously the authors treated the cases of two quadrics and a…

We give new contributions to the existence problem of canonical surfaces of high degree. We construct several families (indeed, connected components of the moduli space) of surfaces $S$ of general type with $p_g=5,6$ whose canonical map has…

The following corollary has been added: for general tetragonal curve $C$ of genus $g\ge 9$ the homogeneous coordinate ring of $C$ defined by the line bundle $K(-T)$, where $K$ is the canonical class, $T$ is the tetragonal series, is Koszul.…

Let $C\subset \mathbb{P}^{g-1}$ be a general curve of genus $g$ and let $k$ be a positive integer such that the Brill-Noether number $\rho(g,k,1)\geq 0$ and $g > k+1$. The aim of this short note is to study the relative canonical resolution…

Let $p: S\to S_g$ be a finite covering of an orientable closed surface of genus $g$. We prove that, for $g\geq 3$, the rational homology group $H_1(S;{\mathbb Q})$ is generated by cycles supported on simple closed curves $\gamma\subset S$…

Let X be a toric variety over a field K determined by a triangle. Let Y be the blow-up at (1,1) in X. In this paper we give some criteria for finite generation of the Cox ring of Y in the case where Y has a curve C such that C^2 \le 0 and…

The conchoid of a plane curve $C$ is constructed using a fixed circle $B$ in the affine plane. We generalize the classical definition so that we obtain a conchoid from any pair of curves $B$ and $C$ in the projective plane. We present two…

Let $C$ be an irreducible projective plane curve in the complex projective space ${\mathbb{P}}^2$. The classification of such curves, up to the action of the automorphism group $PGL(3,{\mathbb{C}})$ on ${\mathbb{P}}^2$, is a very difficult…

Consider modular forms arising from a finite-area quotient of the upper-half plane by a Fuchsian group. By the classical results of Kodaira-Spencer, this ring of modular forms may be viewed as the log spin canonical ring of a stacky curve.…

The family of Euclidean triangles having some fixed perimeter and area can be identified with a subset of points on a nonsingular cubic plane curve, i.e., an elliptic curve; furthermore, if the perimeter and the square of the area are…

Let $S$ be an abelian surface over an algebraically closed field $k$ with characteristic different from $2$ and $3$, and $\mathcal{L}$ a symmetric ample line bundle defining a polarisation of type $(1,3)$. Then the linear system…

We prove that every finitely presentable group G arises as the fundamental group of an orientable 3-complex obtained from a hyperbolic link complement, by coning each boundary torus of the link exterior to a distinct point. We define the…

This paper is concerned with rational curves on real classical groups. Our contributions are three-fold: (i) We determine the structure of quadratic rational curves on real classical groups. As a consequence, we completely classify…