相关论文: Very ample linear series on quadrigonal curves

Given a real curve, we study special linear systems called "very special" for which the dimension does not satisfy a Clifford type inequality. We classify all these very special linear systems when the gonality of the curve is small.

An expository description of smooth cubic curves in the real or complex projective plane.

We study smooth tropical plane quartic curves and show that they satisfy certain properties analogous to (but also different from) smooth plane quartics in algebraic geometry. For example, we show that every such curve admits either…

We enumerate the singular algebraic curves in a complete linear system on a smooth projective surface. The system must be suitably ample in a rather precise sense. The curves may have up to eight nodes, or a triple point of a given type and…

We give a sharp bound on the number of automorphisms of a stable curve of a given genus and describe all curves attaining this bound.

By studying $\mathbb{A}^1$-curves on varieties, we propose a geometric approach to strong approximation problem over function fields of complex curves. We prove that strong approximation holds for smooth, low degree affine complete…

In this article we consider exceptional sequences of invertible sheaves on smooth complete rational surfaces. We show that to every such sequence one can associate a smooth complete toric surface in a canonical way. We use this structural…

We study plane curves over finite fields whose tangent lines at smooth $\mathbb{F}_q$-points together cover all the points of $\mathbb{P}^2(\mathbb{F}_q)$.

We study the family of rational curves on arbitrary smooth hypersurfaces of low degree using tools from analytic number theory.

Orthogonal polynomials on quadratic curves in the plane are studied. These include orthogonal polynomials on ellipses, parabolas, hyperbolas, and two lines. For an integral with respect to an appropriate weight function defined on any…

This is a survey on the Fano schemes of linear spaces, conics, rational curves, and curves of higher genera in smooth projective hypersurfaces, complete intersections, Fano threefolds, etc.

A new family of maximal curves over a finite field is presented and some of their properties are investigated.

In this paper we describe projective curves and surfaces such that almost all their hyperplane sections are projectively equivalent. Our description is complete for curves and close to being complete for smooth surfaces. In the appendix we…

Inspired by very ampleness of Zariski Geometries, we introduce and study the notion of a very ample family of plane curves in any strongly minimal set, and the corresponding notion of a very ample strongly minimal set (characterized by the…

We consider smooth surfaces $S \subset \Pq$ containing a plane curve $P$ and prove some general result concerning the linear system $|H-P|$. We then look at regular surfaces lying on hypersurfaces of degree $s$ having a plane of…

Discrete analogs of extrema of curvature and generalizations of the four-vertex theorem to the case of polygons and polyhedra are suggested and developed. For smooth curves and polygonal lines in the plane, a formula relating the number of…

Let M be a Q-divisor on a smooth surface over C. In this paper we give criteria for very ampleness of the adjoint of the round-up of M. (Similar results for global generation were given by Ein and Lazarsfeld and used in their proof of…

We give necessary and sufficient topological conditions for a simple closed curve on a real rational surface to be approximable by smooth rational curves. We also study approximation by smooth rational curves with given complex…

In this paper we study some properties of surfaces immersed in $\mathbf R ^4$ whose asymptotic lines are orthogonal. We also analyze necessary and sufficient conditions for the hypersphericity of surfaces in $\mathbf R ^4$.

The author determines the structure of automorphism groups of smooth plane curves of degree at least four. Furthermore, he gives some upper bounds for the order of automorphism groups of smooth plane curves and classifies the cases with…