A combinatorial proof of non-speciality of systems with at most 9 imposed base points
It is known that the Segre-Gimigliano-Harbourne-Hirschowitz Conjecture holds for linear systems of curves with at most 9 imposed base fat points. We give a nice proof based on a combinatorial method of showing non-speciality of such systems. We will also prove, by the same method, that systems $math...
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Wydawnictwo Naukowe Uniwersytetu Pedagogicznego
2009-04-01
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| Series: | Annales Universitatis Paedagogicae Cracoviensis: Studia Mathematica |
| Online Access: | http://studmath.up.krakow.pl/index.php/studmath/article/view/87 |
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doaj-37a91b0c789641e99ac119c55d0eb8af2020-11-24T20:40:17ZdeuWydawnictwo Naukowe Uniwersytetu PedagogicznegoAnnales Universitatis Paedagogicae Cracoviensis: Studia Mathematica 2081-545X2009-04-01817990A combinatorial proof of non-speciality of systems with at most 9 imposed base pointsMarcin DumnickiIt is known that the Segre-Gimigliano-Harbourne-Hirschowitz Conjecture holds for linear systems of curves with at most 9 imposed base fat points. We give a nice proof based on a combinatorial method of showing non-speciality of such systems. We will also prove, by the same method, that systems $mathcal L(km;m^{imes k^2})$ and $mathcal L(km+1;m^{imes k^2})$ are non-special.http://studmath.up.krakow.pl/index.php/studmath/article/view/87 |
| collection |
DOAJ |
| language |
deu |
| format |
Article |
| sources |
DOAJ |
| author |
Marcin Dumnicki |
| spellingShingle |
Marcin Dumnicki A combinatorial proof of non-speciality of systems with at most 9 imposed base points Annales Universitatis Paedagogicae Cracoviensis: Studia Mathematica |
| author_facet |
Marcin Dumnicki |
| author_sort |
Marcin Dumnicki |
| title |
A combinatorial proof of non-speciality of systems with at most 9 imposed base points |
| title_short |
A combinatorial proof of non-speciality of systems with at most 9 imposed base points |
| title_full |
A combinatorial proof of non-speciality of systems with at most 9 imposed base points |
| title_fullStr |
A combinatorial proof of non-speciality of systems with at most 9 imposed base points |
| title_full_unstemmed |
A combinatorial proof of non-speciality of systems with at most 9 imposed base points |
| title_sort |
combinatorial proof of non-speciality of systems with at most 9 imposed base points |
| publisher |
Wydawnictwo Naukowe Uniwersytetu Pedagogicznego |
| series |
Annales Universitatis Paedagogicae Cracoviensis: Studia Mathematica |
| issn |
2081-545X |
| publishDate |
2009-04-01 |
| description |
It is known that the Segre-Gimigliano-Harbourne-Hirschowitz Conjecture holds for linear systems of curves with at most 9 imposed base fat points. We give a nice proof based on a combinatorial method of showing non-speciality of such systems. We will also prove, by the same method, that systems $mathcal L(km;m^{imes k^2})$ and $mathcal L(km+1;m^{imes k^2})$ are non-special. |
| url |
http://studmath.up.krakow.pl/index.php/studmath/article/view/87 |
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AT marcindumnicki acombinatorialproofofnonspecialityofsystemswithatmost9imposedbasepoints AT marcindumnicki combinatorialproofofnonspecialityofsystemswithatmost9imposedbasepoints |
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