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- W16789022 abstract "gl. Introduction. . In [5] we gave some examples of rational double points of dimensions >2, which are the quotient spaces by the alternative subgroup of a finite unitary group generated by reflections. These are hypersurface singularities and not isolated singularities. Let x be a point in X, a complex analytic space. In the senseNof [3] x is a rational singular point if, given a resblution of sigularities z:X-X, then (Rh*e7).==O, for i>O. .・ We have a necessary and suthcient criterion for x to be rational that does not involve a priori knowledge of what a resolution of x looks like: Let (o be a holomorphic n-form defined on a deleted neighborhood of xEX, which is nowhere vanishing on this neighborhood. Then xEi¥ is rational if and only if tu is-square integrable in a neighborhood of x (see [3]). In this paper' we show that there exists a nowhere vanishing holomorphic differential form on the quotient space by the alternative subgroup of a finite unitary group generated by reflections. Each of Artin's rational double points has the form of zg=f(2i, 22). By the criterion, to= d2i2A2,dZ2 must be locally square integrable on the variety." @default.
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- W16789022 date "1977-11-01" @default.
- W16789022 modified "2023-09-24" @default.
- W16789022 title "On Nowhere Vanishing Holomorphic Forms of Certain Rational Double Points" @default.
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