Remarks on the existence of Cartier divisors
Stefan Schroeer
TL;DR
This paper investigates when an invertible sheaf corresponds to a Cartier divisor, especially in cases involving embedded components, providing examples and characterizations of such invertible sheaves.
Contribution
It offers new insights and criteria for when invertible sheaves originate from Cartier divisors, addressing cases with embedded components.
Findings
Examples of invertible sheaves not coming from Cartier divisors
Characterization of invertible sheaves that do come from Cartier divisors
Conditions under which the correspondence holds or fails
Abstract
Given an invertible sheaf, does it come from a Cartier divisor? This might fail in presence of embedded components. I give some examples and characterize those invertible sheaves that allow a Cartier divisor.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic Geometry and Number Theory · Meromorphic and Entire Functions