On Seshadri constants of varieties with large fundamental group
نویسندگان
چکیده
منابع مشابه
SESHADRI CONSTANTS ON ABELIAN VARIETIES By MICHAEL NAKAMAYE
We show that on a complex abelian variety of dimension two or greater the Seshadri constant of an ample line bundle is at least one. Moreover, the Seshadri constant is equal to one if and only if the polarized abelian variety splits as a product of a principally polarized elliptic curve and a polarized abelian subvariety of codimension one. We also examine the case when the Seshadri constant is...
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Given a smooth complex projective variety X and an ample line bundle L on X. Fix a point x ∈ X. We consider the question, are there conditions which guarantee the maxima of the Seshadri constant of L at x, i.e ε(L, x) = n √ L? We give a partial answer for surfaces and find examples where the answer to our question is negative. If (X,Θ) is a general principal polarized abelian surface, then ε(Θ,...
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The purpose of this paper is to study the Seshadri constants of abelian varieties. Consider a polarized abelian variety (A,L) of dimension g over the field of complex numbers. One can associate to (A,L) a real number ε(A,L), its Seshadri constant, which in effect measures how much of the positivity of L can be concentrated at any given point of A. The number ε(A,L) can be defined as the rate of...
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In this paper, we associate an invariant αx(L) to an algebraic point x on an algebraic variety X with an ample line bundle L. The invariant α measures how well x can be approximated by rational points on X , with respect to the height function associated to L. We show that this invariant is closely related to the Seshadri constant ǫx(L) measuring local positivity of L at x, and in particular th...
متن کاملSeshadri constants on algebraic surfaces
0. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. Seshadri constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2. Very ample line bundles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3. Bounds on global Seshadri constants . . . . . . . . . . . . . . . . . . . . . . . . 9 4. The degree of sub-maximal cu...
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ژورنال
عنوان ژورنال: ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE
سال: 2019
ISSN: 2036-2145,0391-173X
DOI: 10.2422/2036-2145.201609_012