Sökning: "Algebraic geometry"
Visar resultat 11 - 15 av 76 avhandlingar innehållade orden Algebraic geometry.
11. Topological and geometrical methods in data analysis
Sammanfattning : This thesis concerns two related data analysis pipelines, using topological and geometrical methods respectively, to extract relevant information. The first pipeline, referred to as the topological data analysis (TDA) pipeline, constructs a filtered simplicial complex on a given data set in order to describe its shape. LÄS MER
12. Real and complex Monge-Ampère equations, statistical mechanics and canonical metrics
Sammanfattning : Recent decades has seen a strong trend in complex geometry to study canonical metrics and the way they relate to geometric analysis, algebraic geometry and probability theory. This thesis consists of four papers each contributing to this field. The first paper sets up a probabilistic framework for real Monge-Ampère equations on tori. LÄS MER
13. Multipoint Okounkov bodies
Sammanfattning : During the nineties, the field medallist Okounkov found a way to associate to an ample line bundle L over an n−complex dimensional projective manifold X a convex body in Rn, now called Okounkov body ∆(L). The construction depends on the choice of a valuation centered at one point p∈X and it works even if L is a big line bundle. LÄS MER
14. Multipoint Okounkov bodies, strong topology of ω-plurisubharmonic functions and Kähler-Einstein metrics with prescribed singularities
Sammanfattning : The most classical topic in Kähler Geometry is the study of Kähler-Einstein metrics as solution of complex Monge-Ampère equations. This thesis principally regards the investigation of a strong topology for ω-plurisubharmonic functions on a fixed compact Kähler manifold (X,ω), its connection with complex Monge-Ampère equations with prescribed singularities and the consequent study of singular Kähler-Einstein metrics. LÄS MER
15. Ga-actions on Complex Affine Threefolds
Sammanfattning : This thesis consists of two papers and a summary. The papers both deal with affine algebraic complex varieties, and in particular such varieties in dimension three that have a non-trivial action of one of the one-dimensional algebraic groups Ga := (C, +) and Gm := (C*, ·). LÄS MER
