Maps between non-commutative spaces

Author:
S. Paul Smith

Journal:
Trans. Amer. Math. Soc. **356** (2004), 2927-2944

MSC (2000):
Primary 14A22; Secondary 16S38

DOI:
https://doi.org/10.1090/S0002-9947-03-03411-1

Published electronically:
November 18, 2003

MathSciNet review:
2052602

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a graded ideal in a not necessarily commutative graded -algebra in which for all . We show that the map induces a closed immersion between the non-commutative projective spaces with homogeneous coordinate rings and . We also examine two other kinds of maps between non-commutative spaces. First, a homomorphism between not necessarily commutative -graded rings induces an affine map from a non-empty open subspace . Second, if is a right noetherian connected graded algebra (not necessarily generated in degree one), and is a Veronese subalgebra of , there is a map ; we identify open subspaces on which this map is an isomorphism. Applying these general results when is (a quotient of) a weighted polynomial ring produces a non-commutative resolution of (a closed subscheme of) a weighted projective space.

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Additional Information

**S. Paul Smith**

Affiliation:
Department of Mathematics, Box 354350, University of Washington, Seattle, Washington 98195

Email:
smith@math.washington.edu

DOI:
https://doi.org/10.1090/S0002-9947-03-03411-1

Received by editor(s):
September 18, 2002

Received by editor(s) in revised form:
April 29, 2003

Published electronically:
November 18, 2003

Additional Notes:
The author was supported by NSF grant DMS-0070560

Article copyright:
© Copyright 2003
American Mathematical Society