Projective fibrations in weighted scrolls

Thesis

This thesis studies classification problems of codimension 1 and codimension 2 threefold families

f : X → P^1 , X ⊂ F_A

fibred in low-degree K3 surfaces over P^1 and embedded in weighted scrolls F_A , where A is an integer matrix defining weights and twists. We classify X such as K3 surfaces with rational double points, Calabi–Yau 3-folds with isolated singularities which extend results of Mullet, K3 surfaces and Calabi–Yau 3-folds with at most Gorenstein singularities. Further, the thesis revisits degeneration of quartic K3 fibred Calabi–Yau threefolds studied some time ago by Gross and Ruan.

The thesis also sets the stage for a general study of fibrations embedded in weighted scrolls

( f : X → B) ,→ (π : F_ A → P^{k−1}[c i ])

over any nonsingular base B ⊂ P^{k−1}[c i ] by proposing a multi-graded C-algebra geometry method for constructing them. We initiate the study of fibrations embedded in families of key varieties such as weighted Grassmannians fibrations, leaving detailed investigations for later work.

Authors: Mboya, G

• DOI: 10.5287/ora-2ad4b816e
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: projective fibrations; rational double points; multi-graded C-algebras; scrolls; degenerations; relative key varieties
• Subjects: Classification (Algebraic geometry)