Residue calculus and effective Nullstellensatz
نویسندگان
چکیده
منابع مشابه
Residue Calculus and Effective Nullstellensatz
where h is the maximal size in the sense of Mahler of the pj . There does not seem to exist so far an Arithmetic Division Theory that could provide good estimates for the Faltings heights of the cycles corresponding to qj or for the maximal Mahler size of the qj . Nevertheless, using analytic methods based on the existence of integral representation formulas in Complex Analysis and multidimensi...
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We prove effective Nullstellensatz and elimination theorems for difference equations in sequence rings. More precisely, we compute an explicit function of geometric quantities associated to a system of difference equations (and these geometric quantities may themselves be bounded by a function of the number of variables, the order of the equations, and the degrees of the equations) so that for ...
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We show new upper and lower bounds for the effective differential Nullstellensatz for differential fields of characteristic zero with several commuting derivations. Seidenberg was the first to address this problem in 1956, without giving a complete solution. The first explicit bounds appeared in 2009 in a paper by Golubitsky, Kondratieva, Szanto, and Ovchinnikov,with the upper bound expressed i...
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Improved local and global versions of the effective Nullstellensatz for ideal sheaves on non-singular complex varieties are obtained, based on a new invariant motivated by the notion of finite type from the theory of several complex variables. Two closely related curve selection theorems for curves with maximal adjusted tangency orders to a given ideal sheaf are established along the way, using...
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ژورنال
عنوان ژورنال: American Journal of Mathematics
سال: 1999
ISSN: 1080-6377
DOI: 10.1353/ajm.1999.0026