On rational cuspidal plane curves and the local cohomology of Jacobian rings
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...
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 کاملساختار کلاسهایی از حلقه های z- موضعی و c- موضعی the structure of some classes of z-local and c-local rings
فرض کنیمr یک حلقه تعویض پذیر ویکدار موضعی باشدو(j(r رایکال جیکوبسن r و(z(r مجموعه مقسوم علیه های صفر حلقه r باشد.گوییم r یک حلقه z- موضعی است هرگاه j(r)^2=. .همچنین برای یک حلقه تعویض پذیر r فرض کنیم c یک عنصر ناصفر از (z( r باشد با این خاصیت که cz( r)=0 گوییم حلقه موضعی r یک حلقه c - موضعی است هرگاه و{0 و z(r)^2={cو z(r)^3=0, نیز xz( r)=0 نتیجه دهد که x عضو {c,0 } است. در این پایان نامه ساخ...
Rational 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: Commentarii Mathematici Helvetici
سال: 2019
ISSN: 0010-2571
DOI: 10.4171/cmh/471