6 citations · 15 across the 4 of their papers we have counts for
7 papers
Bounding the number of graph refinements for Brill-Noether existence
Karl Christ, Qixiao Ma
Let be a finite graph of genus . Let and be non-negative integers such that the Brill-Noether number is non-negative. It is known that for some sufficiently larg…
A Clifford inequality for semistable curves
Karl Christ
Let be a semistable curve and a line bundle whose multidegree is uniform, i.e., in the range between those of the structure sheaf and the dualizing sheaf of . We establi…
Degeneration of curves on some polarized toric surfaces
Karl Christ, Xiang He, Ilya Tyomkin
We address the following question: Given a polarized toric surface (S,L), and a general integral curve C of geometric genus g in the linear system |L|, do there exist degenerations…
On the rank of general linear series on stable curves
Karl Christ
We study the dimension of loci of special line bundles on stable curves and for a fixed semistable multidegree. In case of total degree , we characterize when the effect…
On the Severi problem in arbitrary characteristic
Karl Christ, Xiang He, Ilya Tyomkin
In this paper, we show that Severi varieties parameterizing irreducible reduced planar curves of a given degree and geometric genus are either empty or irreducible in any character…
Compactified Jacobians as Mumford models
Karl Christ, Sam Payne, Tif Shen
We show that relative compactified Jacobians of one-parameter smoothings of a nodal curve of genus g are Mumford models of the generic fiber. Each such model is given by an admissi…