Chiral Poincaré duality (Q1574755)

Let \(X\) be a smooth algebraic variety over \(\mathbb{C}\). In this note, a sheaf of vertex superalgebras \(\Omega_X^{ch}\) on \(X\) is introduced. The aim of this note is to prove the following theorem: The space H\(^*(X, \Omega_X^{ch})\) carries a canonical non-degenerate symmetric bilinear form \[ \langle , \rangle:\text{H}^*(X,\Omega_X^{ch}) \times \text{H}^*(X,\Omega_X^{ch}) \to \mathbb{C}. \] This form makes the components of different conformal weights orthogonal and identifies \[ \text{H}^q(X,\Omega_i^{ch,p})^* =\text{H}^{n-q}(X, \Omega_i^{ch,n-p}). \]