AI 中文总结
研究复数域上亏格3曲线模空间，通过特定方法证明其中存在一条亏格105的完备曲线。
AI 中文摘要
我们证明了在复数域上亏格3的光滑射影曲线模空间中，存在一条亏格105的完备曲线。
英文摘要
We show the existence of a complete trigonal curve of geometric genus 10 in the moduli space $\mathcal{M}_3$ of smooth complex projective curves of genus $3$, and of a complete curve of geometric genus 102 through a general point of $\mathcal{M}_3$. We also show that the moduli space $\mathcal{A}_3$ of principally polarized complex abelian threefolds contains a complete curve whose normalization is a hyperelliptic curve of genus 4.
Commentsthis is an improved version of the previous preprint. An ancillary Magma file contains the related computations
