To a smooth variety X with simple normal crossings divisor D, we associate a sheaf of vertex algebras on X, denoted \(\Omega ^{ch}_{X}(\operatorname {log}D)\) , whose conformal weight 0 subspace is the algebra \(\Omega _{X}(\operatorname {log}D)\) of forms with log poles along D. We prove various basic structural results about \(\Omega ^{ch}_{X}(\operatorname {log}D)\) . In particular, if \(X^{*}=X\setminus D\) has a volume form then we show that \(\Omega ^{ch}_{X}(\operatorname {log}D)\) admits a topological structure of rank \(d=\operatorname {dim}(X)\) , which is enhanced to an extended topological structure if \(D\sim -K_{X}\) is in fact anticanonical. In this latter case, we also show that the resulting (q, y) character \(\operatorname {Ell}(X,D)(q,y)\) is a section of the line bundle \(\Theta ^{\otimes d}\) on the elliptic curve \(E=\textbf{C}^{*}/q^{\textbf{Z}}\) . We further show how \(\Omega ^{ch}_{X}(\operatorname {log}D)\) can be understood in terms of a simple birational modification of the space of jets into X.
