Maximal Cohen-Macaulay modules over certain Segre products
Linquan Ma
TL;DR
This paper investigates the existence of maximal Cohen-Macaulay modules over specific Segre product rings, proving non-existence results that challenge existing conjectures and deepen understanding of module theory in algebraic geometry.
Contribution
It provides new non-existence theorems for rank one maximal Cohen-Macaulay modules over certain Segre products, disproving a conjecture by Schoutens.
Findings
No rank one maximal Cohen-Macaulay modules over these rings.
Maximal Cohen-Macaulay modules with low multiplicity do not exist.
Disproves Schoutens' conjecture on module existence.
Abstract
We prove some results on the non-existence of rank one maximal Cohen-Macaulay modules over certain Segre product rings. As an application we show that over these Segre product rings there do not exist maximal Cohen-Macaulay modules with multiplicity less than or equal to the parameter degree of the ring, which disproves a conjecture of Schoutens.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic structures and combinatorial models · Algebraic Geometry and Number Theory