Holme type theorem for special linear groups

2021/04/19 by Kaliman, Shulim
#14E25 #14L30 #14R10 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2104.09550

Abstract

Let Z be an affine algebraic variety and ED(Z)= max(2 dim Z+1, dim TZ). Let X be a smooth algebraic variety isomorphic to a semi-simple linear algebraic group whose Lie algebra is a sum of special linear Lie algebras. We show that if dim X > ED(Z) -1, then Z admits a closed embedding into X. We also show that for every smooth affine flexible variety Y there is a closed embedding of Z into the the product of Y and an affine n-space provided that n > dim Z- 2 and dim Y +n > ED (Z) -1.

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