On Orevkov's rational cuspidal plane curves
نویسندگان
چکیده
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...
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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...
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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...
متن کاملRational torsion in optimal elliptic curves and the cuspidal subgroup
LetN be a square free integer, and let A be an optimal elliptic curve over Q of conductor N . We prove that if A has a rational torsion point of prime order r such that r does not divide 6N , then r divides the order of the cuspidal subgroup of J0(N).
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ژورنال
عنوان ژورنال: Journal of the Mathematical Society of Japan
سال: 2012
ISSN: 0025-5645
DOI: 10.2969/jmsj/06420365