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Topics in computation, numerical methods and algebraic geometryPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2010 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Stockholm: KTH , 2010. , v, 20 p.
##### Series

Trita-MAT. MA, ISSN 1401-2278 ; 10:13
##### National Category

Mathematics
##### Identifiers

URN: urn:nbn:se:kth:diva-25941ISBN: 978-91-7415-770-3 (print)OAI: oai:DiVA.org:kth-25941DiVA: diva2:360978
##### Public defence

2010-11-29, Sal F3, Lindstedtsvägen 26, KTH, Stockholm, 13:00 (English)
##### Opponent

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt472",{id:"formSmash:j_idt472",widgetVar:"widget_formSmash_j_idt472",multiple:true});
##### Supervisors

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt478",{id:"formSmash:j_idt478",widgetVar:"widget_formSmash_j_idt478",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt484",{id:"formSmash:j_idt484",widgetVar:"widget_formSmash_j_idt484",multiple:true});
##### Note

QC 20101115Available from: 2010-11-15 Created: 2010-11-05 Last updated: 2010-11-15Bibliographically approved
##### List of papers

This thesis concerns computation and algebraic geometry. On the computational side we have focused on numerical homotopy methods. These procedures may be used to numerically solve systems of polynomial equations. The thesis contains four papers.

In Paper I and Paper II we apply continuation techniques, as well as symbolic algorithms, to formulate methods to compute Chern classes of smooth algebraic varieties. More specifically, in Paper I we give an algorithm to compute the degrees of the Chern classes of smooth projective varieties and in Paper II we extend these ideas to cover also the degrees of intersections of Chern classes.

In Paper III we formulate a numerical homotopy to compute the intersection of two complementary dimensional subvarieties of a smooth quadric hypersurface in projective space. If the two subvarieties intersect transversely, then the number of homotopy paths is optimal. As an application we give a new solution to the inverse kinematics problem of a six-revolute serial-link mechanism.

Paper IV is a study of curves on certain special quartic surfaces in projective 3-space. The surfaces are invariant under the action of a finite group called the level (2,2) Heisenberg group. In the paper, we determine the Picard group of a very general member of this family of quartics. We have found that the general Heisenberg invariant quartic contains 320 smooth conics and we prove that in the very general case, this collection of conics generates the Picard group.

1. Chern numbers of smooth varieties via homotopy continuation and intersection theory$(function(){PrimeFaces.cw("OverlayPanel","overlay370124",{id:"formSmash:j_idt521:0:j_idt525",widgetVar:"overlay370124",target:"formSmash:j_idt521:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. Computing intersection numbers of Chern classes$(function(){PrimeFaces.cw("OverlayPanel","overlay370129",{id:"formSmash:j_idt521:1:j_idt525",widgetVar:"overlay370129",target:"formSmash:j_idt521:1:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

3. Algebraic C*-actions and inverse kinematics$(function(){PrimeFaces.cw("OverlayPanel","overlay370137",{id:"formSmash:j_idt521:2:j_idt525",widgetVar:"overlay370137",target:"formSmash:j_idt521:2:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

4. Curves on Heisenberg invariant quartic surfaces in projective 3-space$(function(){PrimeFaces.cw("OverlayPanel","overlay370144",{id:"formSmash:j_idt521:3:j_idt525",widgetVar:"overlay370144",target:"formSmash:j_idt521:3:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt1242",{id:"formSmash:lower:j_idt1242",widgetVar:"widget_formSmash_lower_j_idt1242",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt1243_j_idt1245",{id:"formSmash:lower:j_idt1243:j_idt1245",widgetVar:"widget_formSmash_lower_j_idt1243_j_idt1245",target:"formSmash:lower:j_idt1243:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});