2014/10/12 by Marc Coppens, Coppens, Marc
Mathematics · #05C99 #14H51 #14T05 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:05C99 #msc:14H51 #msc:14T05
paper · pdf · doi:10.48550/arxiv.1410.3114
12 pages, 3 figures
arxiv created 2014/10/12 · arxiv updated 2014/10/14
On a metric graph we introduce the notion of a free divisor as a replacement for the notion of a base point free complete linear system on a curve. By means of an example we show that the Clifford inequality is the only obstruction for the existence of very special free divisors on a graph. This is different from the situation of base point free linear systems on curves. It gives rise to the existence of many types of divisors on graphs that cannot be lifted to curves maintaining the rank and it also shows that classifications made for linear systems of some fixed small positive Clifford index do not hold (exactly the same) on graphs.