2011/07/12 by Ein, Lawrence, Ishii, Shihoko, Mustata, Mircea
#14B05 #14F18 #Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1107.2192
We define a version of multiplier ideals, the Mather multiplier ideals, on a variety with arbitrary singularities, using the Mather discrepancy and the Jacobian ideal. In this context we prove a relative vanishing theorem, thus obtaining restriction theorems and a subadditivity and summation theorems. The Mather multiplier ideals also satisfy a Skoda type result. As an application, we obtain a Briancon-Skoda type formula for the integral closures of ideals on a variety with arbitrary singularities.