论文标题
versei曲线尺寸
Severi dimensions for unicuspidal curves
论文作者
论文摘要
我们在存在非基础奇点的情况下，在射影曲线上研究线性序列的参数空间，即{\ it cusps};为此，我们根据Value Semigroup对尖齿进行了分层。我们证明，{\ it概括的severi杂种} $ \ mathbb {p}^1 \ rightArrow \ mathbb {p}^n $，带有固定度和算术属的图像，通常是{\ it {\ it realcible}时，只要$ n \ n \ n \ n \ geq 3 $。我们还证明，在delta-invariant $ g \ ll d $的过度elliptic pusp中，severi的多样性$ d $地图是$ d $ d $ d $ d $ holomorphic maps $ \ holomorphic maps $ \ mathbb {p}^p}^1 \ origharrow \ orightarrow \ oirtarrow \ mathbbbb} n $对于小$ g $，限制是准确的，地图的相应空间是统一地层的不相交联盟。最后，我们猜想了与{\ it nutary}值半群相关的单一质理性曲线的概括。
We study parameter spaces of linear series on projective curves in the presence of unibranch singularities, i.e. {\it cusps}; and to do so, we stratify cusps according to value semigroup. We show that {\it generalized Severi varieties} of maps $\mathbb{P}^1 \rightarrow \mathbb{P}^n$ with images of fixed degree and arithmetic genus are often {\it reducible} whenever $n \geq 3$. We also prove that the Severi variety of degree-$d$ maps with a hyperelliptic cusp of delta-invariant $g \ll d$ is of codimension at least $(n-1)g$ inside the space of degree-$d$ holomorphic maps $\mathbb{P}^1 \rightarrow \mathbb{P}^n$; and that for small $g$, the bound is exact, and the corresponding space of maps is the disjoint union of unirational strata. Finally, we conjecture a generalization for unicuspidal rational curves associated to an {\it arbitrary} value semigroup.
