Saturday, 10 February 2007

ag.algebraic geometry - Permanence of regularity in "generalised" semistable models

Given a regular ring A with an element t, consider the "generalised" semistable model
S:=A[X1,...,Xn]/(P1cdotsPnt) over A, where Pi:=Xiei and ei are positive integers.



Question: For which A, t, and (ei) is S regular?



E.g., when n=2 and A is a discrete valuation ring and t is a uniformiser, then it is easy to prove that S is regular when e1 and e2 are both equal to 1. When nge3 and (A,t) is a DVR with uniformiser t, is there a reference?

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