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
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله

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 XâPS2âS 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
Journal: Advances in Mathematics - Volume 198, Issue 1, 1 December 2005, Pages 366-382
نویسندگان
Michael Artin, Fernando Rodriguez-Villegas, John Tate,