Concave transforms of filtrations and rationality of Seshadri constants
نویسندگان
چکیده
We show that the subgraph of concave transform a multiplicative filtration on section ring is Newton--Okounkov body certain semigroup, and if induced by divisorial valuation, then associated graded algebra sections concrete line bundle in higher dimension. use this description to give rationality criterion for Seshadri constants. Along way we introduce bodies abstract semigroups determine conditions their slices be subsemigroups.
منابع مشابه
Remarks on Seshadri Constants
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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Introduction In this paper we present an alternative approach to the boundedness of Seshadri constants of nef and big line bundles at a general point of a complex–projective variety. Seshadri constants ε(L, x), which have been introduced by Demailly [De92], measure the local positivity of a nef line bundle L at a point x ∈ X of a complex–projective variety X, and can be defined as ε(L, x) := in...
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This numerical definition is equivalent to a more intuitive geometric definition. In particular, ǫ(x,A) is the supremum of all non–negative rational numbers α such that the linear series |nA| separates nα–jets at x for n sufficiently large and divisible. Note that if L is a nef line bundle on X then Definition 1 still makes sense and ǫ(x, L) is defined accordingly. When L is nef but not ample, ...
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One of Demailly’s characterizations of Seshadri constants on ample line bundles works with Lelong numbers of certain positive singular hermitian metrics. In this note sections of multiples of the line bundle are used to produce such metrics and then to deduce another formula for Seshadri constants. It is applied to compute Seshadri constants on blown up products of curves, to disprove a conject...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2021
ISSN: ['2330-0000']
DOI: https://doi.org/10.1090/tran/8345