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In this paper, we briefly survey some developments in gauged linear sigma models (GLSMs). Specifically, we give an overview of progress on constructions of GLSMs for various geometries, GLSM-based computations of quantum cohomology, quantum sheaf cohomology, and quantum K theory rings, as well as two-dimensional abelian and nonabelian mirror constructions.
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On minimal non-σ-scattered linear orders
The purpose of this article is to give new constructions of linear orders which are minimal with respect to being non-σ-scattered. Specifically, we will show that Jensen's diamond principle implies that there is a minimal Countryman line, answering a question of Baumgartner. We also produce the first consistent examples of minimal non-sigma-scattered linear orders of cardinality greater than aleph1, as given a successor cardinal kappa+, we obtain such linear orderings of cardinality kappa+ with the additional property that their square is the union of kappa-many chains. We give two constructions: directly building such examples using forcing, and also deriving their existence from combinatorial principles. The latter approach shows that such minimal non-sigma-scattered linear orders of cardinality kappa+ exist for every infinite cardinal kappa in Gödel's constructible universe, and also (using work of Rinot [28]) that examples must exist at successors of singular strong limit cardinals in the absence of inner models satisfying the existence of a measurable cardinal mu of Mitchell order mu++.
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- PAR ID:
- 10507721
- Publisher / Repository:
- Elsevier
- Date Published:
- Journal Name:
- Advances in Mathematics
- Volume:
- 441
- Issue:
- C
- ISSN:
- 0001-8708
- Page Range / eLocation ID:
- 109540
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1016/j.aim.2024.109540
