Algebraic invariants of projections of varieties and partial elimination ideals

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In this paper, we are interested in the properties of inner and outer projections with a view toward the Eisenbud-Goto regularity conjecture or the characterization of varieties satisfying certain extremal conditions. For example, if X is a quadratic scheme, the depth and regularity X and those of its inner projection from a smooth point are equal. In general, the above equalities do not hold for non-quadratic schemes. Therefore it is natural to investigate the algebraic invariants (e.g., depth and regularity) of X and its projected image in general. We develop a framework which provides partial answers and explains their relations using the partial elimination ideal theory. Our main theorems recover several preceding results in the literature. We also give some interesting examples and applications to illustrate our results. (C) 2021 Elsevier Inc. All rights reserved.
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Issue Date
2021-11
Language
English
Article Type
Article
Citation

JOURNAL OF ALGEBRA, v.586, pp.973 - 1013

ISSN
0021-8693
DOI
10.1016/j.jalgebra.2021.07.019
URI
http://hdl.handle.net/10203/287513
Appears in Collection
MA-Journal Papers(저널논문)
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