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Seshadri-Konstanten auf Abelschen Flächen
In der vorliegenden Arbeit werden Seshadri-Konstanten auf abelschen Flächen untersucht. Auf abelschen Flächen mit Picardzahl 1 gelang es Bauer (1999) die Seshadri-Konstanten vollständig zu berechnen. In den verbleibenden Picardzahlen 2, 3 und 4 lagen bisher nur Ergebnisse zu einigen Selbstprodukten...
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| フォーマット: | Dissertation |
| 言語: | ドイツ語 |
| 出版事項: |
Philipps-Universität Marburg
2021
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| オンライン･アクセス: | PDFフルテキスト |
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In the present thesis, Seshadri constants on abelian surfaces are studied. On abelian surfaces with Picard number 1, Bauer (1999) succeeded in computing all Seshadri constants. In the remaining cases, only some self-products of elliptic curves were solved by Bauer and Schulz (2008). In this thesis, new methods are developed which enable the calculation of all Seshadri constants on abelian surfaces with Picard number 2 and even plot the Seshadri function. The methods also give some insight on the structure of the Seshadri function and reveal that the Seshadri function is of the same baffling complexity as the Cantor function. In Picard number 3 and 4, further results are obtained for products of elliptic curves by considering and completly answering the question whether all Seshadri constants are intergers.