Page 1

Displaying 1 – 3 of 3

Showing per page

The moduli space of commutative algebras of finite rank

Bjorn Poonen (2008)

Journal of the European Mathematical Society

The moduli space of rank- n commutative algebras equipped with an ordered basis is an affine scheme 𝔅 n of finite type over , with geometrically connected fibers. It is smooth if and only if n 3 . It is reducible if n 8 (and the converse holds, at least if we remove the fibers above 2 and 3 ). The relative dimension of 𝔅 n is 2 27 n 3 + O ( n 8 / 3 ) . The subscheme parameterizing étale algebras is isomorphic to GL n / S n , which is of dimension only n 2 . For n 8 , there exist algebras that are not limits of étale algebras. The dimension calculations...

Currently displaying 1 – 3 of 3

Page 1