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Full-Text Articles in Algebraic Geometry
Computing Intersection Multiplicity Via Triangular Decomposition, Paul Vrbik
Computing Intersection Multiplicity Via Triangular Decomposition, Paul Vrbik
Electronic Thesis and Dissertation Repository
Fulton’s algorithm is used to calculate the intersection multiplicity of two plane curves about a rational point. This work extends Fulton’s algorithm first to algebraic points (encoded by triangular sets) and then, with some generic assumptions, to l many hypersurfaces.
Out of necessity, we give a standard-basis free method (i.e. practically efficient method) for calculating tangent cones at points on curves.
Tilting Sheaves On Brauer-Severi Schemes And Arithmetic Toric Varieties, Youlong Yan
Tilting Sheaves On Brauer-Severi Schemes And Arithmetic Toric Varieties, Youlong Yan
Electronic Thesis and Dissertation Repository
The derived category of coherent sheaves on a smooth projective variety is an important object of study in algebraic geometry. One important device relevant for this study is the notion of tilting sheaf.
This thesis is concerned with the existence of tilting sheaves on some smooth projective varieties. The main technique we use in this thesis is Galois descent theory. We first construct tilting bundles on general Brauer-Severi varieties. Our main result shows the existence of tilting bundles on some Brauer-Severi schemes. As an application, we prove that there are tilting bundles on an arithmetic toric variety whose toric variety …