On the rank of general linear series on stable curves

Abstract We study the dimension of loci special line bundles on stable curves and for a fixed semistable multidegree. In case total degree $$d = g - 1$$ d = g - 1 , we characterize when effective locus gives Theta divisor. $$g 2$$ 2 show that is either empty or has expected dimension. This leads to new characterization semistability in these degrees. remaining cases, codimension at least 2. If multidegree addition non-negative each irreducible component curve, contains an irrreducible