On the moduli space of 𝜆-connections,Proceedings of the American Mathematical Society

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On the moduli space of 𝜆-connections
Proceedings of the American Mathematical Society ( IF 0.8 ) Pub Date : 2020-11-30 , DOI: 10.1090/proc/15279
Anoop Singh

Abstract:Let

be a compact Riemann surface of genus $g \geq 3$ . Let $\mathcal {M}_{Hod}$ denote the moduli space of stable $\lambda$ -connections over

and let $\mathcal {M}'_{Hod} \subset \mathcal {M}_{Hod}$ denote the subvariety whose underlying vector bundle is stable. Fix a line bundle

of degree zero. Let $\mathcal {M}_{Hod}(L)$ denote the moduli space of stable $\lambda$ -connections with fixed determinant

and let $\mathcal {M}'_{Hod}(L) \subset \mathcal {M}_{Hod}(L)$ be the subvariety whose underlying vector bundle is stable. We show that there is a natural compactification of $\mathcal {M}'_{Hod}$ and $\mathcal {M}'_{Hod} (L)$ and study their Picard groups. Let $\mathbb{M}_{Hod}(L)$ denote the moduli space of polystable $\lambda$ -connections. We investigate the nature of algebraic functions on $\mathcal {M}_{Hod}(L)$ and $\mathbb{M}_{Hod}(L)$ . We also study the automorphism group of $\mathcal {M}'_{Hod}(L)$ .

中文翻译：

𝜆-连接的模空间

摘要：让

一个紧的黎曼曲面 $g \ geq 3$ 。令其表示稳定连接的模空间，并令其底层向量束稳定的子变量。固定零度线束。令其表示行列式稳定的稳定连接的模空间，并令其为底层向量束稳定的子变量。我们发现，有一个自然紧致和学习他们的皮卡德组。让我们分别表示polystable的模空间-connections。我们研究的代数函数的性质和。我们还研究的自同构群。 $\ mathcal {M} _ {Hod}$ $\ lambda$

$\ mathcal {M}'_ {Hod} \ subset \ mathcal {M} _ {Hod}$

$\ mathcal {M} _ {Hod}（L）$ $\ lambda$

$\ mathcal {M}'_ {Hod}（L）\ subset \ mathcal {M} _ {Hod}（L）$ $\ mathcal {M}'_ {Hod}$ $\ mathcal {M}'_ {Hod}（L）$ $\ mathbb {M} _ {Hod}（L）$ $\ lambda$ $\ mathcal {M} _ {Hod}（L）$ $\ mathbb {M} _ {Hod}（L）$ $\ mathcal {M}'__ Hod}（L）$

更新日期：2021-02-02

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