Saturday, 10 February 2007

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

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



Question: For which AA, tt, and (ei)(ei) is SS regular?



E.g., when n=2n=2 and AA is a discrete valuation ring and tt is a uniformiser, then it is easy to prove that SS is regular when e1e1 and e2e2 are both equal to 1. When nge3nge3 and (A,t)(A,t) is a DVR with uniformiser tt, is there a reference?

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