论文标题
通过节俭的乐高建筑，带有$ρ<0 $的线性系列
Linear series with $ρ< 0$ via thrifty lego-building
论文作者
论文摘要
Moduli空间$ \ MATHCAL {g}^r_ {g，d} \ to \ Mathcal {m} _g $参数化gengebraic curves具有线性系列$ d $ and等级$ r $预期相对尺寸$ρ= g-（r+1）（r+1）（g -d+r）$。经典的Brill-Noether理论涉及$ρ\ geq 0 $;我们认为非拆卸案例$ρ<0 $。当$ 0>ρ\ geq -g + 3 $ $ 0>ρ\ geq -g + 3 $或$ 0>ρ\ geq -c_r g + \ mathcal {o}（g^{5/6}）$时，根据$ c_r $ c_的级别，我们证明了该模块空间的组件存在，并具有预期的相对维度。 \ infty $。这些结果通过适用于电感参数的两标记概括和极限线性序列的再生定理证明。
The moduli space $\mathcal{G}^r_{g,d} \to \mathcal{M}_g$ parameterizing algebraic curves with a linear series of degree $d$ and rank $r$ has expected relative dimension $ρ= g - (r+1)(g-d+r)$. Classical Brill-Noether theory concerns the case $ρ\geq 0$; we consider the non-surjective case $ρ< 0$. We prove the existence of components of this moduli space with the expected relative dimension when $0 > ρ\geq -g+3$, or $0 > ρ\geq -C_r g + \mathcal{O}(g^{5/6})$, where $C_r$ is a constant depending on the rank of the linear series such that $C_r \to 3$ as $r \to \infty$. These results are proved via a two-marked-point generalization suitable for inductive arguments, and the regeneration theorem for limit linear series.
