Title: The Deligne-Riemann-Roch isomorphism Show Chinese title

Title: 德林-黎曼-罗赫同构

Abstract: This paper is the second in a series devoted to Deligne's conjectural program on refined versions of the Grothendieck-Riemann-Roch theorem via the determinant of the cohomology. We prove a general form of the Deligne-Riemann-Roch isomorphism, lifting the degree-one part of the Grothendieck-Riemann-Roch formula to a canonical isomorphism of line bundles. This extends previous constructions and is formulated and proven in a flexible reinterpretation of Elkik's theory of intersection bundles introduced in the first paper of the series. This resolves the geometric aspect of Deligne's program. Among the applications, we derive a natural isomorphism relating the BCOV bundle and the Hodge bundle of a family of Calabi-Yau varieties, which is part of the mathematical formulation of the genus one mirror symmetry conjecture proposed in a previous work with Mourougane. Show Chinese abstract

Abstract: 本文是系列文章的第二篇，致力于通过上同调的行列式来研究Deligne关于Grothendieck-Riemann-Roch定理精化版本的猜想计划。 我们证明了Deligne-Riemann-Roch同构的一般形式，将Grothendieck-Riemann-Roch公式的次数一部分提升为线丛的规范同构。 这扩展了以前的构造，并在系列第一篇文章中引入的Elkik交类理论的灵活重释中进行表述和证明。 这解决了Deligne计划中的几何方面。 在应用中，我们推导出一个自然同构，将BCOV包与Calabi-Yau流形族的Hodge包联系起来，这是与Mourougane之前合作工作中提出的 genus one mirror symmetry 猜想的数学表述的一部分。