Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
Results
Showing 1 to 7 of 7 for “"resolution of singularities"”.
-
Equivariant resolution of singularities and semi-stable reduction in characteristic 0
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1997.
-
The structure of spaces of valuations and the local uniformization problem
The problem of resolution of singularities is a major problem in algebraic geometry. Local uniformization can be seen as its local version. For varieties over fields of characteristic zero, local uniformization was proved by Zariski in 1940 and resolution of singularities was proved by Hironaka in …
-
Sharp estimates for trilinear oscillatory integral forms
This dissertation consists of 4 chapters. In Chapter 1, we will briefly introduce some background of the trilinear oscillatory integrals and the motivations for their study. We also outline some key ideas in their proofs, as well as the major novelty of this dissertation. Chapter 2 serves as …
-
Geometric Theory of Parshin Residues
In the early 70's Parshin introduced his notion of the multidimensional residues of meromorphic top-forms on algebraic varieties. Parshin's theory is a generalization of the classical one-dimensional residue theory. The main difference between the Parshin's definition and the one-dimensional case …
-
Deformation invariance of rational pairs
… by Kollár and Kovács, generalize rational singularities to pairs (X,D). Here X is a normal variety and D is a reduced divisor on X. Integral to the definition of a rational pair is the notion of a thrifty resolution, also defined by Kollár and Kovács, and in order to work with rational …
-
Mirrors to Toric Degenerations via Intrinsic Mirror Symmetry
… symmetry. After briefly exploring the case of degenerations of elliptic curves, we show that the Gross-Siebert mirror construction for minimal relative log Calabi-Yau degenerations generalizes that for divisorial toric degenerations $\bar{\mathfrak{X}} \to \mathcal{S}$ of K3-s that have a …
-
Quantum Corrected and Nonsingular Black Holes: Theoretical and Phenomenological Aspects
General Relativity is a cornerstone of modern physics and has now achieved the status of precision science. Despite its success in explaining a wide range of phenomena, significant open questions remain about the fundamental nature of gravity. These unresolved issues suggest the need for a quantum …