Publication Date

9-5-2013

Abstract

Links of isolated singularities defined by weighted homogeneous polynomials have a natural Sasakian structure. Since it is known that Sasaki-Einstein metrics have positive Ricci curvature, and since positive Sasakian structures give rise to Sasakian metrics with positive Ricci curvature, it is useful to determine which links have a positive Sasakian structure. This corresponds to the Fano index of the associated weighted projective variety being positive. Links of dimension $2n-1$ are $(n-2)$-connected. In dimension 5, there is a complete classification of simply connected spin manifolds due to Smale. Hypersurface singularities yielding links of dimension 5 have been treated by Boyer, Galicki, Koll\'{a}r, Nakamaye, and others. This paper investigates isolated singularities of codimension 2 complete intersections with 5 dimensional links of positive index and provides a complete list up to degree 600, hence a complete (up to degree 600) list of types of links having positive Sasakian structures.

Degree Name

Mathematics

Level of Degree

Doctoral

Department Name

Mathematics & Statistics

First Committee Member (Chair)

Charles Boyer

Second Committee Member

Ivan Cheltsov

Third Committee Member

Michael Nakamaye

Fourth Committee Member

Dimiter Vassilev

Language

English

Keywords

Sasakian Structures, Einstein Metrics, Weighted Projective Varieties, Links of Singularities, Complete Intersections

Document Type

Dissertation

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