模顶点代数的共形块
Conformal blocks for modular vertex algebras
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中文总结 AI 辅助
本文研究了模顶点代数的共形块理论，将其从复数域推广到任意代数闭域，并移除了 $C_1$-cofinite 和 CFT 型等标准假设，从而扩展了该理论的适用范围。
中文摘要 AI 辅助
给定一个在 $\mathbb{C}$ 上的顶点算子代数 $V$，已知如何在稳定、$n$ 个标记点、亏格为 $g$ 的曲线的模空间 $\overline{\mathcal{M}}_{g,n}$ 上定义所谓的余不变量层和共形块。我们将此理论推广到配备有在任何代数闭域上的坐标变换概念的顶点代数。作为我们论证的副产品，我们还表明这些构造中的一些标准假设可以被移除，例如 $C_1$-cofinite 或 CFT 型。
英文摘要
Given a vertex operator algebra $V$ over $\mathbb{C}$, it is known how to define so-called sheaves of coinvariants and conformal blocks on the moduli space $\overline{\mathcal{M}}_{g,n}$ of stable, $n$-pointed, genus $g$ curves. We extend this theory to vertex algebras equipped with a notion of change of coordinates over any algebraically closed field. As a by-product of our arguments, we also show that a number of standard assumptions in these constructions can be removed, such as being $C_1$-cofinite or CFT-type.
