• Login
    View Item 
    •   Home
    • Research
    • Articles
    • View Item
    •   Home
    • Research
    • Articles
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Browse

    All of KAUSTCommunitiesIssue DateSubmit DateThis CollectionIssue DateSubmit Date

    My Account

    Login

    Quick Links

    Open Access PolicyORCID LibguidePlumX LibguideSubmit an Item

    Statistics

    Display statistics

    Algorithms for singularities and real structures of weak Del Pezzo surfaces

    • CSV
    • RefMan
    • EndNote
    • BibTex
    • RefWorks
    Type
    Article
    Authors
    Lubbes, Niels
    KAUST Department
    Computer Science Program
    Visual Computing Center (VCC)
    Date
    2014-08
    Preprint Posting Date
    2013-02-27
    Permanent link to this record
    http://hdl.handle.net/10754/563664
    
    Metadata
    Show full item record
    Abstract
    In this paper, we consider the classification of singularities [P. Du Val, On isolated singularities of surfaces which do not affect the conditions of adjunction. I, II, III, Proc. Camb. Philos. Soc. 30 (1934) 453-491] and real structures [C. T. C. Wall, Real forms of smooth del Pezzo surfaces, J. Reine Angew. Math. 1987(375/376) (1987) 47-66, ISSN 0075-4102] of weak Del Pezzo surfaces from an algorithmic point of view. It is well-known that the singularities of weak Del Pezzo surfaces correspond to root subsystems. We present an algorithm which computes the classification of these root subsystems. We represent equivalence classes of root subsystems by unique labels. These labels allow us to construct examples of weak Del Pezzo surfaces with the corresponding singularity configuration. Equivalence classes of real structures of weak Del Pezzo surfaces are also represented by root subsystems. We present an algorithm which computes the classification of real structures. This leads to an alternative proof of the known classification for Del Pezzo surfaces and extends this classification to singular weak Del Pezzo surfaces. As an application we classify families of real conics on cyclides. © World Scientific Publishing Company.
    Citation
    LUBBES, N. (2014). ALGORITHMS FOR SINGULARITIES AND REAL STRUCTURES OF WEAK DEL PEZZO SURFACES. Journal of Algebra and Its Applications, 13(05), 1350158. doi:10.1142/s0219498813501582
    Sponsors
    It is my pleasure to acknowledge that the many computations with Josef Schicho is a major contribution to this paper. Also he recognized the Pappus configuration of Example 7. I would like to thank Michael Harrison for useful discussions concerning root subsystems. I would like to thank Ulrich Derenthal for informing me of a mistake in a previous version of this paper. The algorithms were implemented using the computer algebra system Sage ([18]). This research was supported by the Austrian Science Fund (FWF): project P21461.
    Publisher
    World Scientific Pub Co Pte Lt
    Journal
    Journal of Algebra and Its Applications
    DOI
    10.1142/S0219498813501582
    arXiv
    1302.6678
    Additional Links
    http://arxiv.org/abs/arXiv:1302.6678v5
    ae974a485f413a2113503eed53cd6c53
    10.1142/S0219498813501582
    Scopus Count
    Collections
    Articles; Computer Science Program; Visual Computing Center (VCC)

    entitlement

     
    DSpace software copyright © 2002-2021  DuraSpace
    Quick Guide | Contact Us | Send Feedback
    Open Repository is a service hosted by 
    Atmire NV
     

    Export search results

    The export option will allow you to export the current search results of the entered query to a file. Different formats are available for download. To export the items, click on the button corresponding with the preferred download format.

    By default, clicking on the export buttons will result in a download of the allowed maximum amount of items. For anonymous users the allowed maximum amount is 50 search results.

    To select a subset of the search results, click "Selective Export" button and make a selection of the items you want to export. The amount of items that can be exported at once is similarly restricted as the full export.

    After making a selection, click one of the export format buttons. The amount of items that will be exported is indicated in the bubble next to export format.