The asymptotic growth of equivariant sections of positive and big line bundles

نویسنده

  • Roberto Paoletti
چکیده

υ(X,L) = lim sup k→∞ n! kn h(X,OX(kL)). If L is ample, or more generally nef and big, υ(L) = (L), the self-intersection number of L. The volume of a general big line bundle has been studied in [F] and [DEL]; in particular, υ(L) has been given the following geometric interpretation (Proposition 3.6 of [DEL]): Let (kL) [n] be the moving selfintersection number of kL, that is, the number of intersection points away from the base locus of n general divisors in the linear series |kL|. Then

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Balanced Line Bundles and Equivariant Compactifications of Homogeneous Spaces

Manin’s conjecture predicts an asymptotic formula for the number of rational points of bounded height on a smooth projective variety X in terms of global geometric invariants of X. The strongest form of the conjecture implies certain inequalities among geometric invariants of X and of its subvarieties. We provide a general geometric framework explaining these phenomena, via the notion of balanc...

متن کامل

Asymptotics and Dimensional Dependence of the Number of Critical Points of Random Holomorphic Sections

Abstract. We prove two conjectures from [DSZ2, DSZ3] concerning the expected number of critical points of random holomorphic sections of a positive line bundle. We show that, on average, the critical points of minimal Morse index are the most plentiful for holomorphic sections of O(N) → CPm and, in an asymptotic sense, for those of line bundles over general Kähler manifolds. We calculate the ex...

متن کامل

Independence of an Equivariant and Invariant‎ Functions in Generalized Normal Family‎

In this paper we explain a necessary and sufficent condition for independence between any arbitrary statistics with sufficient statistics which is also maximum likelihood estimator in a general‎ ‎exponential family with location and scale parameter namely generalized normal distribution‎. ‎At the end‎, ‎it is shown that the converse is true except in the asymptotic cases‎.

متن کامل

Volumes of Line Bundles

In this note we describe the asymptotic growth of the number of global sections of line bundles on surfaces. Beside working out concrete examples, we also show that this quantity does not change in a locally polynomial manner on threefolds. 1991 MSC classification: 14C40 (primary), 14J05, 32C10 (secondary)

متن کامل

Construction of Equivariant Vector Bundles

Let X be the wonderful compactification of a complex adjoint symmetric space G/K such that rk(G/K) = rk(G) − rk(K). We show how to extend equivariant vector bundles on G/K to equivariant vector bundles on X , generated by their global sections and having trivial higher cohomology groups. This relies on a geometric construction of equivariant vector bundles in the setting of varieties with reduc...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2002