Some remarks on associated varieties of vertex operator superalgebras

We study several families of vertex operator superalgebras from a jet (super)scheme point view. provide new examples algebras which are “chiral-quantizations" their $$C_{2}$$ -algebras $$R_V$$ . Our come affine $$C_\ell ^{(1)}$$ -series algebras, $$\ell \geqslant 1$$ , certain $$N=1$$ superconformal Feigin–Stoyanovsky principal subspaces, type graph $$W_{\Gamma }$$ and extended Virasoro algebras. also give counterexample to the chiral-quantization property for $$N=2$$ algebra with central charge 1.