Two new papers on essential dimension

Updated June 10, 2016

I have two new papers out, both joint with Bob Guralnick:

  • Spinors and essential dimension: We show that certain representations of the spin group Spinn are generically free for n > 14 and calculate the generic stabilizer for n ≤ 14, for all base fields. This shows that the formula for the essential dimension of spin groups in characteristic zero also holds in all characteristics other than 2.
  • Essential dimension of algebraic groups, including bad characteristic: This paper, originally with a different title (“exceptional” instead of “algebraic”) gives upper bounds for the essential dimension of a split simple algebraic group over an algebraically closed field.  The novelty is that all groups are included and all characteristics are allowed, and that the bounds are as good as or better than the previous best known bounds over the complex numbers.  The proofs are by proving that certain representations are generically free.  This paper will be published in Archiv der Mathematik.