منابع مشابه
F -thresholds of Hypersurfaces
In characteristic zero one can define invariants of singularities using all divisors over the ambient variety. A key result that makes these invariants computable says that they can be determined by the divisors on a resolution of singularities. For example, if a is a sheaf of ideals on a nonsingular variety, then to every nonnegative real number λ one associates the multiplier ideal J (a). The...
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For a Noetherian local domain (R, m, K), it is an open question whether strong F–regularity deforms. We provide an affirmative answer to this question when the canonical module satisfies certain additional assumptions. The techniques used here involve passing to a Gorenstein ring, using an anti– canonical cover.
متن کاملGood filtrations and F -purity of invariant subrings
Let k be an algebraically closed field of positive characteristic, G a reductive group over k, and V a finite dimensional G-module. Let B be a Borel subgroup of G, and U its unipotent radical. We prove that if S = SymV has a good filtration, then SU is F -pure. Throughout this paper, p denotes a prime number. Let k be an algebraically closed field of characteristic p, and G a reductive group ov...
متن کاملFailure of F-purity and F-regularity in Certain Rings of Invariants
Let Fq be a finite field of characteristic p, K a field containing it, and R = K[X1, . . . , Xn] a polynomial ring in n variables. The general linear group GLn(Fq) has natural action on R by degree preserving ring automorphisms. L. E. Dickson showed that the subring of elements which are fixed by this group action is a polynomial ring, [Di], though for an arbitrary subgroupG of GLn(Fq), the str...
متن کاملHomaloidal hypersurfaces and hypersurfaces with vanishing Hessian
We introduce various families of irreducible homaloidal hypersurfaces in projective space Pr, for all r ≥ 3. Some of these are families of homaloidal hypersurfaces whose degrees are arbitrarily large as compared to the dimension of the ambient projective space. The existence of such a family solves a question that has naturally arisen from the consideration of the classes of homaloidal hypersur...
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ژورنال
عنوان ژورنال: Mathematical Research Letters
سال: 2012
ISSN: 1073-2780,1945-001X
DOI: 10.4310/mrl.2012.v19.n2.a11