Year: 2025
Type: article
Abstract: To a smooth variety X with simple normal crossings divisor D , we associate a sheaf of vertex algebras on X , denoted $$\Omega ^{ch}_{X}(\operatorname {log}D)$$ Ω X ch ( log D ) , whose conformal weight 0 subspace is the algebra $$\Omega _{X}(\operatorname {log}D)$$ Ω X ( log D ) of forms with log poles along D . We prove various basic structural results about $$\Omega ^{ch}_{X}(\operatorname {log}D)$$ Ω X ch ( log D ) . In particular, if $$X^{*}=X\setminus D$$ X ∗ = X \ D has a volume form then we show that $$\Omega ^{ch}_{X}(\operatorname {log}D)$$ Ω X ch ( log D ) admits a topological structure of rank $$d=\operatorname {dim}(X)$$ d = dim ( X ) , which is enhanced to an extended topological structure if $$D\sim -K_{X}$$ D ∼ - K X is in fact anticanonical. In this latter case, we also show that the resulting ( q , y ) character $$\operatorname {Ell}(X,D)(q,y)$$ Ell ( X , D ) ( q , y ) is a section of the line bundle $$\Theta ^{\otimes d}$$ Θ ⊗ d on the elliptic curve $$E=\textbf{C}^{*}/q^{\textbf{Z}}$$ E = C
Source: Annales Henri Poincaré
Author: Emile Bouaziz
Institution: Academia Sinica
Language: Latvian
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
Funder: Academia Sinica
OpenAlex ID: W4414715404