Tautological Ring of the Moduli Space of Generalised Parabolic Line Bundles on a Curve

In this article, we consider the tautological ring containing the extended Brill–Noether algebraic classes on the normalization of the compactified Jacobian of a complex nodal projective curve (with one node). This smallest ?-subalgebra of algebraic classes under algebraic equivalence, stable under extensions of the maps induced by multiplication maps, Pontrayagin product and Fourier transform, is shown to be generated by pullback of the Brill–Noether classes of the Jacobian of the normalized curve and some natural classes.