کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
401301 675331 2010 89 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Application of computational invariant theory to Kobayashi hyperbolicity and to Green–Griffiths algebraic degeneracy
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر هوش مصنوعی
پیش نمایش صفحه اول مقاله
Application of computational invariant theory to Kobayashi hyperbolicity and to Green–Griffiths algebraic degeneracy
چکیده انگلیسی

A major unsolved problem (according to Demailly (1997)) towards the Kobayashi hyperbolicity conjecture in optimal degree is to understand jet differentials of germs of holomorphic discs that are invariant under any reparametrization of the source. The underlying group action is not reductive, but we provide a complete algorithm to generate all invariants, in arbitrary dimension n and for jets of arbitrary order k.Two main new situations are studied in great detail. For jets of order 4 in dimension 4, we establish that the algebra of Demailly–Semple invariants is generated by 2835 polynomials, while the algebra of bi-invariants is generated by 16 mutually independent polynomials sharing 41 Gröbnerized syzygies. Nonconstant entire holomorphic curves valued in an algebraic 3-fold (resp. 4-fold)X3⊂P4(C) (resp. X4⊂P5(C)) of degree d satisfy global differential equations as soon as d⩾72 (resp. d⩾259). A useful asymptotic formula for the Euler–Poincaré characteristic of Schur bundles in terms of Giambelli’s determinants is derived.For jets of order 5 in dimension 2, we establish that the algebra of Demailly–Semple invariants is generated by 56 polynomials, while the algebra of bi-invariants is generated by 17 mutually independent polynomials sharing 105 Gröbnerized syzygies.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Symbolic Computation - Volume 45, Issue 10, October 2010, Pages 986-1074