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

The elliptic algebras in the title are connected graded $\mathbb{C}$-algebras, denoted $Q_{n,k}(E,\tau)$, depending on a pair of relatively prime integers $n>k\ge 1$, an elliptic curve $E$, and a point $\tau\in E$. This paper examines a…

We prove that the canonical ring of a smooth projective variety is finitely generated.

We give a proof of Iitaka's Conjecture C_{2,1} using only elementary methods from algebraic geometry. The main point is that, given a non-isotrivial and relatively minimal family f : X \to B, where X is a surface and B is a curve, both…

For any (unital) exchange ring $R$ whose finitely generated projective modules satisfy the separative cancellation property ($A\oplus A\cong A\oplus B\cong B\oplus B$ implies $A\cong B$), it is shown that all invertible square matrices over…

Let $C$ be a smooth complex projective curve with canonical divisor $K_C$ very ample. We explore the relation between the cup-product $$ H^1 (\Theta_C ) \longrightarrow (H^0({\cal O}_C (K_C))^{\ast} \otimes H^1 ({\cal O}_C) $$ where…

We construct the canonical structure of an irreducible projective variety on the set of connected curves of degree $d$ in $\Bbb P^n$ with rational components (some components can be multiple). The set of rational curves is open subset in…

We show that the endomorphism ring of any nonzero finitely generated projective module over the Leavitt path algebra $L_K(E)$ of an arbitrary graph $E$ with coefficients in a field $K$ is isomorphic to a Steinberg algebra. This yields in…

In this paper I investigate minimal surfaces of general type with p_g=5, q=0 for which the 1-canonical map is a birational morphism onto a surface in P^4 (so called canonical surfaces in P^4) via a structure theorem for the Hilbert…

Let $H$ be obtained from a cyclically $4$-edge-connected cubic planar graph $Y$ other than $K_4$ by deleting two adjacent vertices. We provide a short proof that if $H$ has circumference at least $k$ for some even integer $k \ge 4$, then…

Let $(X,L)$ be a polarized K3 surface of genus $g$ and $C_{en} \subset X$ be the curve of singular points of nodal elliptic curves in $|L|$. When $(X,L)$ is generic of genus two, Huybrechts observed that the curve $C_{en}$ is a constant…

We consider threefolds that admit a fibration by K3 surfaces over a nonsingular curve, equipped with a divisorial sheaf that defines a polarisation of degree two on the general fibre. Under certain assumptions on the threefold we show that…

We construct C*-diagonals with connected spectra in all classifiable stably finite C*-algebras which are unital or stably projectionless with continuous scale. For classifiable stably finite C*-algebras with torsion-free $K_0$ and trivial…

In this paper, we give explicit equations for homogeneous spaces corresponding to a rational isogeny of degree $3$. An explicit set of elliptic curves with elements of order $3$ in their Tate-Shafarevich group is constructed. Combining this…

A point $p$ on a smooth complex projective curve $C$ of genus $g>3$ is subcanonical if the divisor $(2g-2)p$ is canonical. In the moduli space of pointed curves, the subcanonical locus is described by pairs $(C,p)$ as above, and it consists…

Generalizing the classical theorems of Max Noether and Petri, we describe generators and relations for the canonical ring of a stacky curve, including an explicit Gr\"obner basis. We work in a general algebro-geometric context and treat log…

We resolve a case of the oriented knot complement conjecture by showing that knots in an orientable circle bundle $N$ over a genus $g \geq 2$ surface $S$ are determined by their complements. We apply this to the setting of canonical knots…

Let $C$ be a smooth curve of genus $g\ge 4$ and Clifford index $c$. In this paper, we prove that if $C$ is neither hyperelliptic nor bielliptic with $g\ge 2c+5$ and $\mathcal M$ computes the Clifford index of $C$, then either $\deg \mathcal…

The \emph{canonical degree} of a curve $C$ on a surface $X$ is $K_X\cdot C$. Our main result, is that on a surface of general type there are only finitely many curves with negative self--intersection and sufficiently large canonical degree.…

K\"onig's lemma is a fundamental result about trees with countless applications in mathematics and computer science. In contrapositive form, it states that if a tree is finitely branching and well-founded (i.e. has no infinite paths), then…

A one-degree-of-freedom graph is a graph obtained from a minimally rigid graph in the plane and removing an edge. For such graph, the set of realisations with fixed edge length, modulo rotations and reflections, is an algebraic curve. The…