Hirzebruch-Riemann-Roch formulae on irreducible symplectic Kähler manifolds
Hirzebruch-Riemann-Roch formulae on irreducible symplectic Kähler manifolds
In this article we investigate Hirzebruch-Riemann-Roch formulae for line bundles on irreducible symplectic Kähler manifolds. As Huybrechts has shown, for every irreducible symplectic Kähler manifold $X$ of dimension $2n$, there are numbers $a_0, a_2, \dots , a_{2n}$ such that \begin{equation*} \chi (L) = \sum _{k = 0}^n \frac {a_{2k}}{(2k)!} q_X(c_1(L))^k …