  In previous work, we defined certain virtual fundamental classes for special
cycles on the moduli stack of Hermitian shtukas, and related them to the higher
derivatives of non-singular Fourier coefficients of Siegel-Eisenstein series.
In the present article, we construct virtual fundamental classes in greater
generality, including those expected to relate to the higher derivatives of
singular Fourier coefficients. We assemble these classes into "higher" theta
series, which we conjecture to be modular. Two types of evidence are presented:
structural properties affirming that the cycle classes behave as conjectured
under certain natural operations such as intersection products, and
verification of modularity in several special situations. One innovation
underlying these results is a new approach to special cycles in terms of
derived algebraic geometry.
