Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Let $R$ be an integral domain, "nice" (regular for instance). Consider a homomorphism $$ f: R^m \to R^m $$ of two rank $m$ free $R$ modules. Assume that $\ker f =0$ and that the cokernel is $M$. Now let $I$ be the second Fitting ideal of $f$, i.e. the ideal generated by $(m-1) \times (m-1)$ minors of $f$ (write $f$ in terms of an $m \times m$ matrix). The homomorphism $f$ induces $ (R/I)^m \to (R/I)^m$ whose kernel is denoted by $K$ and cokernel is $M/IM$.

The question is: can you construct a canonical homomorphism $$ Hom_{R/I}(I/I^2, R/I) \to Hom_{R/I}(K, M/IM) $$

This question is extracted from the algebro-geometric situation concerning the normal bundle of the determinantal varieties.

share|improve this question
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.