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Integral points on a del Pezzo surface over imaginary quadratic fields

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

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  • Judith Lena Ortmann

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OriginalspracheEnglisch
Aufsatznummer90
Seitenumfang32
FachzeitschriftResearch in Number Theory
Jahrgang10
Ausgabenummer4
PublikationsstatusVeröffentlicht - 8 Nov. 2024

Abstract

Chambert-Loir and Tschinkel constructed a framework for a geometric interpretation of the density of integral points on certain varieties, which was refined by Wilsch. By using harmonic analysis and the circle method, it was proved for some partial equivariant compactifications of vector groups over arbitrary number fields and high-dimensional complete intersections over Q. Further, there are some examples of using the torsor method for singular del Pezzo surfaces over Q. In this paper, we generalise the torsor method for integral points from Q to imaginary quadratic number fields. As a first representative example, we characterise integral points of bounded log-anticanonical height on a quartic del Pezzo surface of singularity type A3 over imaginary quadratic fields with respect to its singularity and its lines. Furthermore, we count these integral points of bounded height by using universal torsors and interpret the count geometrically to prove an analogue of Manin’s conjecture for the set of integral points with respect to the singularity and to a line. Our results coincide with the predicted framework.

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Integral points on a del Pezzo surface over imaginary quadratic fields. / Ortmann, Judith Lena.
in: Research in Number Theory, Jahrgang 10, Nr. 4, 90, 08.11.2024.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Ortmann JL. Integral points on a del Pezzo surface over imaginary quadratic fields. Research in Number Theory. 2024 Nov 8;10(4):90. doi: 10.48550/arXiv.2307.12877, 10.1007/s40993-024-00572-z
Ortmann, Judith Lena. / Integral points on a del Pezzo surface over imaginary quadratic fields. in: Research in Number Theory. 2024 ; Jahrgang 10, Nr. 4.
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