کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
9518161 1345529 2005 17 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On the Jacobians of plane cubics
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
On the Jacobians of plane cubics
چکیده انگلیسی
Let S be a scheme and f a ternary cubic form whose ten coefficients are sections of OS without common zero. The equation f=0 defines a family of plane cubic curves X⊂PS2→S parametrized by S. We prove that the family of generalized Jacobians of those cubic curves is a group scheme J/S which is the locus of smoothness of a scheme f*=0, where f* is a Weierstrass cubic formf*=f*(x,y,z)=y2z+a1xyz+a2yz2-x3-a2x2z-a4xz2-a6z3, in which the coefficient ai is a homogeneous polynomial with integral coefficients, of degree i in the ten coefficients of f, which we give explicitly. A key ingredint of the proof is a characterization, over sufficiently nice bases, of group algebraic spaces which can be described by such a Weierstrass equation.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 198, Issue 1, 1 December 2005, Pages 366-382
نویسندگان
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