ar X iv : a lg - g eo m / 9 70 30 29 v 1 2 1 M ar 1 99 7 GENERIC HYPERSURFACE SINGULARITIES
ثبت نشده
چکیده
The problem considered here can be viewed as the analogue in higher dimensions of the one variable polynomial interpolation of Lagrange and Newton. Let x 1 ,. .. , x r be closed points in general position in projective space P n , then the linear subspace V of H 0 (P n , O(d)) (the space of homogeneous polynomials of degree d on P n) formed by those polynomials which are singular at each x i , is given by r(n + 1) linear equations in the coefficients, expressing the fact that the polynomial vanishes with its first derivatives at x 1 ,. .. , x r. As such, the " expected " value for the dimension of V is max(0, h 0 (O(d)) − r(n + 1)). We prove that V has the " expected " dimension for d ≥ 5 (theorem A.). This theorem was first proven in [A] using a very complicated induction with many initial cases. Here we give a greatly simplified proof using techniques developped by the authors while treating the corresponding problem in lower degrees.
منابع مشابه
ar X iv : a lg - g eo m / 9 70 30 04 v 1 5 M ar 1 99 7 Geometry of Moduli Spaces of Flat Bundles on Punctured Surfaces
For a Riemann surface with one puncture we consider moduli spaces of flat connections such that the monodromy transformation around the puncture belongs to a given conjugacy class with the property that a product of its distinct eigenvalues is not equal to 1 unless we take all of them. We prove that these moduli spaces are smooth and their natural closures are normal with rational singularities.
متن کاملar X iv : a lg - g eo m / 9 70 70 16 v 1 2 5 Ju l 1 99 7 RATIONAL CURVES ON QUASI - PROJECTIVE SURFACES
§
متن کاملar X iv : a lg - g eo m / 9 41 00 29 v 1 2 7 O ct 1 99 4 Contractions on a manifold polarized by an ample vector bundle
متن کامل
ar X iv : a lg - g eo m / 9 70 70 07 v 1 9 J ul 1 99 7 SYMPLECTIC DEFORMATIONS OF CALABI – YAU THREEFOLDS
متن کامل
ar X iv : a lg - g eo m / 9 70 30 11 v 1 9 M ar 1 99 7 Moduli of flat bundles on open Kähler manifolds .
We consider the moduli space MN of flat unitary connections on an open Kähler manifold U (complement of a divisor with normal crossings) with restrictions on their monodromy transformations. Using intersection cohomology with degenerating coefficients we construct a natural closed 2-form F on MN . When U is quasi-projective we prove that F is actually a Kähler form.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1997