论文标题
在$λ$ - 连接的模量空间上
On the Moduli space of $λ$-connections
论文作者
论文摘要
令$ x $为紧凑的Riemann Surface $ g \ geq 3 $。令$ \ cat {m} _ {hod} $表示稳定的$λ$ -Connections $ x $和$ x $和$ \ cat {m}'_ {hod} \ subset \ cat {m} _ {m} _ {hod} $表示子的subsvarieper的模量空间。修复零度的线束$ l $。令$ \ cat {m} _ {hod}（l）$表示稳定的$λ$ - 连接的模量空间，带有固定的确定性$ l $和$ \ cat {m}'_ {hod}（hod}（l）\ subset \ subset \ subset \ cat {m} _ {m} _ {hod} _ {hod} _ {hod}（hod}（hod}）$ bun undle suf sub suply surndle wht suply stute wht verty wht verty wht verty wond verty wht verty wht ver。我们表明，$ \ cat {m}'_ {hod} $和$ \ cat {m}'_ _ {hod}（l）$的天然紧凑型，并研究他们的picard群体。令$ \ m_ {hod}（l）$表示polystable $λ$ - 连接的模量空间。我们在$ \ cat {m} _ {hod}（l）$和$ \ m_ {hod}（l）$上研究了代数函数的性质。我们还研究了$ \ cat {m}'_ {hod}（l）$的自动形态组。
Let $X$ be a compact Riemann surface of genus $g \geq 3$. Let $\cat{M}_{Hod}$ denote the moduli space of stable $λ$-connections over $X $ and $\cat{M}'_{Hod} \subset \cat{M}_{Hod}$ denote the subvariety whose underlying vector bundle is stable. Fix a line bundle $L$ of degree zero. Let $\cat{M}_{Hod}(L)$ denote the moduli space of stable $λ$-connections with fixed determinant $L$ and $\cat{M}'_{Hod}(L) \subset \cat{M}_{Hod}(L)$ be the subvariety whose underlying vector bundle is stable. We show that there is a natural compactification of $\cat{M}'_{Hod}$ and $\cat{M}'_{Hod} (L)$, and study their Picard groups. Let $\M_{Hod}(L)$ denote the moduli space of polystable $λ$-connections. We investigate the nature of algebraic functions on $\cat{M}_{Hod}(L)$ and $\M_{Hod}(L)$. We also study the automorphism group of $\cat{M}'_{Hod}(L)$.
