منابع مشابه
Rational Cuspidal Curves
It is the product of my playing with beautiful geometric objects called rational cuspidal curves over the past two years. I would like to thank everyone who has contributed to this thesis. I owe so much to everyone who has ever taught me mathematics. Thank you for inspiring me and for providing me with the skills necessary to complete this thesis. To my friends and fellow students at Abel, than...
متن کاملOn the Number of the Cusps of Rational Cuspidal Plane Curves
A cuspidal curve is a curve whose singularities are all cusps, i.e. unibranched singularities. The article describes computations which lead to the following conjecture: A rational cuspidal plane curve of degree greater or equal to six has at most three cusps. The curves with precisely three cusps occur in three series. Assuming the Flenner–Zaidenberg rigidity conjecture the above conjecture is...
متن کاملDiffeomorphisms, Isotopies, and Braid Monodromy Factorizations of Plane Cuspidal Curves
In this paper we prove that there is an infinite sequence of pairs of plane cuspidal curves Cm,1 and Cm,2, such that the pairs (CP, Cm,1) and (CP, Cm,2) are diffeomorphic, but Cm,1 and Cm,2 have non-equivalent braid monodromy factorizations. These curves give rise to the negative solutions of ”Dif=Def” and ”Dif=Iso” problems for plane irreducible cuspidal curves. In our examples, Cm,1 and Cm,2 ...
متن کاملBraid Monodromy Type and Rational Transformations of Plane Algebraic Curves
We combine the newly discovered technique, which computes explicit formulas for the image of an algebraic curve under rational transformation, with techniques that enable to compute braid monodromies of such curves. We use this combination in order to study properties of the braid monodromy of the image of curves under a given rational transformation. A description of the general method is give...
متن کاملRational torsion in elliptic curves and the cuspidal subgroup
Let A be an elliptic curve over Q of square free conductor N . Suppose A has a rational torsion point of prime order r such that r does not divide 6N . We prove that then r divides the order of the cuspidal subgroup C of J0(N). If A is optimal, then viewing A as an abelian subvariety of J0(N), our proof shows more precisely that r divides the order of A ∩ C. Also, under the hypotheses above, we...
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ژورنال
عنوان ژورنال: Mathematische Nachrichten
سال: 2000
ISSN: 0025-584X,1522-2616
DOI: 10.1002/(sici)1522-2616(200002)210:1<93::aid-mana93>3.0.co;2-4