منابع مشابه
On submaximal plane curves
We prove that a submaximal curve in P has sequence of multiplicities (μ, ν, . . . , ν), with μ < sν for every integer s with (s− 1)(s+ 2) ≥ 6.76( r − 1). This note is a sequel to [10], where a specialization method was developed in order to bound the degree of singular plane curves. The problem under consideration is, given a system of multiplicities (m) = (m1,m2, . . . ,mr) ∈ Z and points p1, ...
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We study some properties of generator sequences of planar semigroups and give a method of construction of plane curves with one place at infinity with given generator sequences. We also discuss similar questions for polynomial curves. ∗We express our deep gratitude and appreciation for to Professor Shreeram S. Abhyankar for being a constant source of our mathematical inspiration.
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Let V be a generic quintic threefold in the 4-dimensional complex projective space P. A well-known conjecture of Clemens says that V has only a finite number of rational curves in each degree. Although Clemens’ conjecture is still quite open at this moment (it is known to be true for degree up to 7 by S. Katz [K]), recently physicists, based on the mirror symmetry principle, have proposed a for...
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In this thesis we will have a look at algebraic curves in the projective plane over an arbitrary algebraically closed field k. Using the resultant of polynomial rings over k we define intersection multiplicities and prove Bézout’s Theorem for effective divisors. We define singularities and inflexion points and count their number depending on the degree of the curve, using the Hessian of a curve.
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This problem is related to a conjecture of Kobayashi and Zaidenberg which states that for a sufficiently general curve D ⊂ P of degree d ≥ 5, as general in the sense that D lies in |OP2(d)| ∼= P d(d+3)/2 with countably many closed proper subvarieties removed, the affine variety P\D is hyperbolic. One necessary condition for P\D being hyperbolic is that there is no rational curve C ⊂ P meeting D...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2004
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2003.11.010