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Reduction to Directrix-near points in resolution of singularities of schemes

Voitovitch, Alexander (2016) Reduction to Directrix-near points in resolution of singularities of schemes. PhD, Universität Regensburg.

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Date of publication of this fulltext: 04 Feb 2016 12:07

Abstract (English)

By a result by Cossart, Jannsen and Saito, for a blow-up X' of a locally noetherian scheme X in a permissible center D, every point x' of X', which is near to a point x of D, lies in the projective space, associated the directrix at x, if the dimension of X is at most two. We show that this holds for dimension up to five under an additional assumption on the dimension of the ridges at x' and x, and get an application to resolution of singularities.

Translation of the abstract (German)

Nach einem Resultat von Cossart, Jannsen und Saito, liegt bei einer Aufblasung X' eines noetherschen Schemas X in einem zulässigen Zentrum D jeder Punkt x' von X, der nah zu einem Punkt x von D ist, auf dem zur Direktrix bei x assoziierten projektiven Raum, falls die Dimension von X höchstens zwei ist. Wir zeigen, dass dies für ein bis zu fünfdimensionales Schema X gilt unter einer zusätzlichen ...

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Item type:Thesis of the University of Regensburg (PhD)
Date:4 February 2016
Referee:Prof. Dr. Uwe Jannsen
Date of exam:10 December 2015
Institutions:Mathematics > Prof. Dr. Uwe Jannsen
Classification:
NotationType
14B05MSC
14E15MSC
14L10MSC
Keywords:algebraic geometry, resolution of singularities, blow-up, ridge, directrix
Dewey Decimal Classification:500 Science > 510 Mathematics
Status:Published
Refereed:Yes, this version has been refereed
Created at the University of Regensburg:Yes
Item ID:33216
Owner only: item control page

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