ar X iv : 0 70 5 . 12 10 v 2 [ m at h . A G ] 1 8 Ju l 2 00 7 F - THRESHOLDS OF HYPERSURFACES
نویسنده
چکیده
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 jumping exponents of a are those λ such that J (a) 6= J (a ′ ) for every λ < λ. It is an easy consequence of the formula giving the multiplier ideals of f in terms of a log resolution of singularities, that the jumping exponents form a discrete set of rational numbers. See for example [Laz], Ch. 9 for the basic facts about multiplier ideals and their jumping exponents.
منابع مشابه
ar X iv : m at h / 02 07 25 7 v 1 [ m at h . A G ] 2 7 Ju l 2 00 2 RATIONAL CURVES ON HYPERSURFACES OF LOW DEGREE , II
This is a continuation of [7] in which we proved irreducibility of spaces of rational curves on a general hypersurface X d ⊂ P n of degree d < n+1 2. In this paper, we prove that if d 2 + d + 2 ≤ n and if d ≥ 3, then the spaces of rational curves are themselves rationally connected.
متن کاملar X iv : 0 80 7 . 00 58 v 2 [ m at h . D G ] 1 6 Ju l 2 00 8 EQUIVARIANT DIFFERENTIAL CHARACTERS AND SYMPLECTIC REDUCTION
We describe equivariant differential characters (classifying equi-variant circle bundles with connections), their prequantization, and reduction.
متن کاملar X iv : 0 70 7 . 40 46 v 1 [ m at h . A G ] 2 7 Ju l 2 00 7 CLIFFORD ’ S THEOREM FOR COHERENT SYSTEMS
Let C be an algebraic curve of genus g ≥ 2. We prove an analogue of Clifford’s theorem for coherent systems on C and some refinements using results of Re and Mercat.
متن کاملar X iv : 0 70 7 . 09 70 v 2 [ m at h . G R ] 1 8 Ju l 2 00 7 Non - abelian free groups admit non - essentially free actions on rooted
We show that every finitely generated non-abelian free group Γ admits a spherically transitive action on a rooted tree T such that the action of Γ on the boundary of T is not essentially free. This reproves a result of Bergeron and Gaboriau. The existence of such an action answers a question of Grigorchuk, Nekrashevich and Sushchanskii.
متن کامل