A Remark on Letzter-Makar-Lirnanov Invariants

摘要

Let X be an irreducible affine algebraic curve over C with normalization (X-tilde), and let D(X) be the ring of (global) differential operators on X . Due to general results of Smith and Stafford (see [SS]), it is known that D(X) is Morita equivalent to D((X-tilde)) if (and only if) the normalization map π: (X-tilde) → X is injective. In the special case when X is rational and (X-tilde) is isomorphic to the affine line A~1, there exist non-isomorphic curves with isomorphic rings of differential operators (the first examples of this kind were found in [L]).