Extremal Rees algebras
Copyright policy )Extremal Rees algebras
We study almost complete intersections ideals whose Rees algebras are extremal in the sense that some of their fundamental metrics---depth or relation type---have maximal or minimal values in the class. The focus is on those ideals that lead to almost Cohen--Macaulay algebras and our treatment is wholly concentrated on the nonlinear relations of the algebras. Several classes of such algebras are presented, some of a combinatorial origin. We offer a different prism to look at these questions with accompanying techniques. The main results are effective methods to calculate the invariants of these algebras.
29 pages
- Rutgers, The State University of New Jersey United States
- Universidade Federal de Pernambuco Brazil
- Universidade Federal de Pernambuco Brazil
- UNIVERSIDADE DE SAO PAULO Brazil
- Southern Connecticut State University United States
13D02, Sally module, birational mapping, Castelnuovo regularity, Morphisms of commutative rings, Commutative Algebra (math.AC), Syzygies, resolutions, complexes and commutative rings, FOS: Mathematics, 13H15, 13B10, 13D02, 13H10, 13H15, 14E05, extremal Rees algebra, almost complete intersection, Rees algebra, Almost complete intersection, 13H10, Multiplicity theory and related topics, 14E05, Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.), relation type, Mathematics - Commutative Algebra, 13B10, almost Cohen-Macaulay algebra, Hilbert function, module of nonlinear relations, Rational and birational maps
13D02, Sally module, birational mapping, Castelnuovo regularity, Morphisms of commutative rings, Commutative Algebra (math.AC), Syzygies, resolutions, complexes and commutative rings, FOS: Mathematics, 13H15, 13B10, 13D02, 13H10, 13H15, 14E05, extremal Rees algebra, almost complete intersection, Rees algebra, Almost complete intersection, 13H10, Multiplicity theory and related topics, 14E05, Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.), relation type, Mathematics - Commutative Algebra, 13B10, almost Cohen-Macaulay algebra, Hilbert function, module of nonlinear relations, Rational and birational maps
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