论文标题
关于稳定曲线的一般线性系列的等级
On the rank of general linear series on stable curves
论文作者
论文摘要
我们研究了稳定曲线和固定的半固定多曲线的特殊线束基因座的尺寸。如果总数$ d = g -1 $，我们表明有效的基因座给出theta除数。如果学位$ g -2 $和$ g $，我们表明该基因座是空的，要么具有预期的维度。这导致了这些程度中的可准性的新表征。在剩下的情况下，我们表明特殊基因座具有至少$ 2 $。如果另外的多种曲线在曲线的每个不可还原成分上都是不负的，我们表明特殊的基因座包含预期维度的不可偿还成分。
We study the dimension of loci of special line bundles on stable curves and for a fixed semistable multidegree. In case of total degree $d = g - 1$, we characterize when the effective locus gives a Theta divisor. In case of degree $g - 2$ and $g$, we show that the locus is either empty or has the expected dimension. This leads to a new characterization of semistability in these degrees. In the remaining cases, we show that the special locus has codimension at least $2$. If the multidegree in addition is non-negative on each irreducible component of the curve, we show that the special locus contains an irrreducible component of expected dimension.
