Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

When does one use infinitesimal deformation (over the ring of dual numbers $k[t]/(t^2)$) versus local deformation (over $k[t]$ or $k[t_1,\ldots, t_n]$)?

It seems that one works over the ring of dual numbers in order to remove or obtain certain singularities (or to compute for degenerate schemes) while one of the reasons one works over $k[t]$ or $k[t_1,\ldots, t_n]$ is to study and relate fibers over various base points, assuming that the ring of interest is a free $k[t]$ or $k[t_1,\ldots, t_n]$-module.

Would you say that this correct?

$$ $$

$$ $$

share|improve this question

1 Answer 1

up vote 0 down vote accepted

I think what I wrote above is correct since $k[x,y]/(xy)$ has a 1-dimensional space of deformations over the dual numbers.

$$ $$ This link is also helpful.

share|improve this answer

Your Answer


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

Not the answer you're looking for? Browse other questions tagged or ask your own question.