
arXiv: 1001.1095
We describe two situations where adding the adjoint divisor to a divisor D with smooth normalization yields a free divisor. Both also involve stability or versality. In the first, D is the image of a corank one stable germ of a map from complex n-space to complex (n+1)-space, and is not free. In the second, D is the discriminant of a versal deformation of a weighted homogeneous function with isolated critical point (subject to certain numerical conditions on the weights). Here D itself is already free. We also prove an elementary result, inspired by these first two, from which we obtain a plethora of new examples of free divisors. The presented results seem to scratch the surface of a more general phenomenon that is still to be revealed.
24 pages, 1 figure
Mathematics - Algebraic Geometry, 32S25, 17B66, 32Q26, 32S30, 14M17, FOS: Mathematics, Algebraic Geometry (math.AG)
Mathematics - Algebraic Geometry, 32S25, 17B66, 32Q26, 32S30, 14M17, FOS: Mathematics, Algebraic Geometry (math.AG)
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