The topology of terminal quartic 3-folds
Anne-Sophie Kaloghiros
TL;DR
This thesis investigates the geometric properties and bounds related to the defect of terminal Gorenstein quartic 3-folds and other Fano 3-folds, providing insights into their non Q-factoriality.
Contribution
It establishes bounds on the defect of terminal Gorenstein quartic 3-folds and explores the geometric reasons for non Q-factoriality in these varieties.
Findings
Bound on the defect of terminal Gorenstein quartic 3-folds
Relationship between defect and non Q-factoriality
Geometric motivation for non Q-factoriality in quartics
Abstract
In this thesis, I determine a bound on the defect of terminal Gorenstein quartic 3-folds. More generally, I study the defect of terminal Gorenstein Fano 3-folds of Picard rank 1 and genus at least 3. I state a geometric "motivation" of non Q-factoriality in the case of quartics.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Rings, Modules, and Algebras · Algebraic structures and combinatorial models