Fake weighted projective spaces

Abstract

We define fake weighted projective spaces as a generalisation of weighted projective spaces. We introduce the notions of fundamental group in codimension 1 and of universal covering in codimension 1. We prove that for every fake weighted projective space its universal cover in codimension 1 is a weighted projective space.

20 pages, master thesis defended at Warsaw University in June 2002

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• On the Integral Cohomology Ring of Toric Orbifolds and Singular Toric Varieties
• Mutations of fake weighted projective planes
• Z-linear Gale duality and poly weighted spaces (PWS)
• Classifying terminal weighted projective space
• The nonequivariant coherent-constructible correspondence and tilting
• Mutations of Fake Weighted Projective Spaces
• Ehrhart polynomial roots of reflexive polytopes
• Sharp bounds on fake weighted projective spaces with canonical singularities
• Inertia groups of a toric DM stack, fake weighted projective spaces, and labelled sheared simplices
• Toric spaces and face enumeration on simplicial manifolds
• Quasismoooth hypersurfaces in toric varieties