Related papers: Simple limit linear series for curves of compact t…

Our aim in this work is to study exact Osserman limit linear series on curves of compact type $X$ with three irreducible components. This case is quite different from the case of two irreducible components studied by Osserman. For instance,…

We investigate the connection between Osserman limit series (on curves of pseudocompact type) and Amini-Baker limit linear series (on metrized complexes with corresponding underlying curve) via a notion of pre-limit linear series on curves…

We introduce a notion of limit linear series for nodal curves which are not of compact type. We give a construction of a moduli space of limit linear series, which works also in smoothing families, and we prove a corresponding…

In the present paper we investigate conditions for the non-existence of a limit linear series on a curve of compact type such that two smooth curves are bridged by a chain of two elliptic curves. Combining this work with results on the…

We investigate limit linear series on chains of elliptic curves, giving a simple proof of a conjecture of Farkas stating the existence of curves with a theta-characteristic with a given number of sections for the expected range of genera.…

We study the limiting case of the Krichever construction of orthogonal curvilinear coordinate systems when the spectral curve becomes singular. We show that the case when the curve is reducible and all its irreducible components are…

We introduce the notion of level-$\delta$ limit linear series, which describe limits of linear series along families of smooth curves degenerating to a singular curve $X$. We treat here only the simplest case where $X$ is the union of two…

We give a practical formula for counting irreducible nodal genus-three plane curves that a fixed generic complex structure on the normalization. As an intermediate step, we enumerate rational plane curves that have a $(3,4)$-cusp.

Let $C$ be a smooth, absolutely irreducible genus-$3$ curve over a number field $M$. Suppose that the Jacobian of $C$ has complex multiplication by a sextic CM-field $K$. Suppose further that $K$ contains no imaginary quadratic subfield. We…

Very few examples of obstructed equsingular families of curves on surfaces other than the projective plane are known. Combining results from Westenberger and Hirano with an idea from math.AG/9802009 we give in the present paper series of…

We propose a combinatorial method of proving non-specialty of a linear system of curves with multiple points in general positions. As an application we obtain a classification of special linear systems on P1xP1 for which the multiplicities…

In the 80's D. Eisenbud and J. Harris considered the following problem: ``What are the limits of Weierstrass points in families of curves degenerating to stable curves?'' But for the case of stable curves of compact type, treated by them,…

Over the past 20 years, a great deal of work has been done on the moduli spaces of coherent systems on algebraic curves. Until recently, however, there has been very little work on the fixed determinant case, except for the special case of…

We introduce a formalism of descent of moduli spaces, and use it to produce limit linear series moduli spaces for families of curves in which the components of fibers may have monodromy. We then construct a universal stack of limit linear…

A linear system of plane curves satisfying multiplicity conditions at points in general position is called special if the dimension is larger than the expected dimension. A (-1) curve is an irreducible curve with self intersection -1 and…

In this note we focus on the defect of singular plane curve that was recently introduced by Dimca. Roughly speaking, the defect of a reduced plane curve measures the discrepancy from the property of being a free curve. We find some…

I study Gromov-Hausdorff limits of complex curves endowed with singular flat metrics of constant diameter. I formulate a criterion that the limit is collapsed in terms of a certain piecewise affine weight function on the dual intersection…

For a given graph whose edges are labeled with general real numbers, we consider the set of functions from the vertex set into the Euclidean plane such that the distance between the images of neighbouring vertices is equal to the…

We obtain exact, simple and very compact expressions for the linearization coefficients of the products of orthogonal polynomials; both the conventional Clebsch-Gordan-type and the modified version. The expressions are general depending…

The dimension of spaces of global sections for line bundles on semistable curves parametrized by the compactified Picard scheme is studied. The theorem of Riemann is shown to hold. The theorem of Clifford is shown to hold in the following…