Cutting diagram method for systems of plane curves with base points
نویسندگان
چکیده
منابع مشابه
Linear Systems of Plane Curves with Base Points of Equal Multiplicity
In this article we address the problem of computing the dimension of the space of plane curves of degree d with n general points of multiplicity m. A conjecture of Harbourne and Hirschowitz implies that when d ≥ 3m, the dimension is equal to the expected dimension given by the Riemann-Roch Theorem. Also, systems for which the dimension is larger than expected should have a fixed part containing...
متن کاملStanford Algebraic Geometry — Seminar — LINEAR SYSTEMS OF PLANE CURVES WITH BASE POINTS OF BOUNDED MULTIPLICITY
We address the problem of computing the dimension of the space of plane curves of fixed degree and general multiple base points. A conjecture of Harbourne and Hirschowitz gives geometric meaning to when this dimension is larger than the expected dimension obtained from Riemann-Roch; specifically, the dimension is larger than expected if and only if the system has a multiple (−1)-curve in its ba...
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Fixing n general points pi in the plane, what is the dimension of the space of plane curves of degree d having multiplicity mi at pi for each i? In this article we propose an approach to attack this problem, and demonstrate it by successfully computing this dimension for all n and for mi constant, at most 3. Our approach is based on an analysis of the corresponding linear system on a degenerati...
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In this paper we investigate some plane curves with many points over Q, finite fields and cyclotomic fields. In a previous paper [4] the first two authors constructed a sequence of absolutely irreducible polynomials Pd(x, y) ∈ Z[x, y] of degree d having low height and many integral solutions to Pd(x, y) = 0. (The definition of these polynomials will be recalled in §4.) Here we construct further...
متن کاملSingular Points of Plane Curves
ly isomorphic to (C×)r−1 × (C), and hence also to (S1)r−1 × (R), where r = |J | is the number of branches and k = δ(C)− r+1 = 1 2 (μ(C) + 1 − r). The construction of the Jacobian variety J(C̃) of the non-singular curve C̃ in the large is standard in algebraic geometry. There is also a notion of Jacobian of a singular curve C , defined e.g. in [85], which, like the other, is an abelian group. Ther...
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ژورنال
عنوان ژورنال: Annales Polonici Mathematici
سال: 2007
ISSN: 0066-2216,1730-6272
DOI: 10.4064/ap90-2-3