GIT for $\hat{U}$-actions on algebraic $\mathbb{C}$-schemes

Abstract

We extend the $\hat{U}$-theorem for projective varieties proved in arXiv:1601.00340 and arXiv:1607.04181 to projective schemes over $\mathbb{C}$. The condition "ss=s" required in arXiv:1601.00340 and arXiv:1607.04181 is reformulated algebraically for our setting. We also describe a blowing up for the condition "ss=s". Different from the sequence of blowing ups in arXiv:1607.04181 , we can get "ss=s" in one blowing up.