Naïve noncommutative blowups at zero-dimensional schemes
نویسندگان
چکیده
منابع مشابه
Naïve Noncommutative Blowups at Zero-dimensional Schemes
In an earlier paper [KRS] we defined and investigated the properties of the näıve blowup of an integral projective scheme X at a single closed point. In this paper we extend those results to the case when one näıvely blows up X at any suitably generic zero-dimensional subscheme Z. The resulting algebra A has a number of curious properties; for example it is noetherian but never strongly noether...
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R = R(X,Z,L, σ) = H(X, R) = k ⊕H(X, R1)⊕H(X, R2)⊕ · · · By [RS2, Theorem 3.1], R is noetherian with qgr-R ' qgr-R. Proposition 1.2. [RS2, Proposition 3.20]. Keep the above assumptions and assume that L is also ample and generated by its global sections. Then there exists M ∈ N such that, for m ≥M : (1) In ⊗ L⊗m n is generated by its global sections for all n ≥ 1. (2) R(X,Z,L⊗m, σ) is generated ...
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In an earlier paper [KRS] we defined and investigated the properties of the na¨ıve blowup of an integral projective scheme X at a single closed point. In this paper we extend those results to the case when one na¨ıvely blows up X at any suitably generic zero-dimensional subscheme Z. The resulting algebra A has a number of curious properties; for example it is noetherian but never strongly noeth...
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We define the Frobenius morphism of certain class of noncommutative blowups in positive characteristic. Thanks to a nice property of the class, the defined morphism is always flat. Therefore we say that the noncommutative blowups in this class are Kunz regular. One of such blowups is the one associated to a regular Galois alteration. From de Jong’s theorem, we see that for every variety over an...
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This paper is a natural continuation of Abbott et al. (2000) further generalizing the Buchberger-Möller algorithm to zero-dimensional schemes in both affine and projective spaces. We also introduce a new, general way of viewing the problems which can be solved by the algorithm: an approach which looks to be readily applicable in several areas. Implementation issues are also addressed, especiall...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2007
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2007.02.017