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代数幾何学セミナー
過去の記録 ～05/01｜次回の予定｜今後の予定 05/02～
| 開催情報 | 金曜日 13:30～15:00 数理科学研究科棟(駒場) 118号室 |
|---|---|
| 担当者 | 權業 善範、河上 龍郎 、榎園 誠 |
2024年11月15日(金)
13:30-15:00 数理科学研究科棟(駒場) 118号室
谷本祥 氏 (名古屋大学)
The spaces of rational curves on del Pezzo surfaces via conic bundles
谷本祥 氏 (名古屋大学)
The spaces of rational curves on del Pezzo surfaces via conic bundles
[ 講演概要 ]
There have been extensive activities on counting functions of rational points of bounded height on del Pezzo surfaces, and one of prominent approaches to this problem is by the usage of conic bundle structures on del Pezzo surfaces. This leads to upper and lower bounds of correct magnitude for quartic del Pezzo surfaces.
In this talk, I will explain how conic bundle structures on del Pezzo surfaces induce fibration structures on the spaces of rational curves on such surfaces. Then I will explain applications of this structure which include:
1. upper bounds of correct magnitude for the counting function of rational curves on quartic del Pezzo surfaces over finite fields.
2. rationality of the space of rational curves on a quartic del Pezzo surface.
Finally, I will explain our ongoing proof of homological stability for the spaces of rational curves on quartic del Pezzo surfaces. This is joint work in progress with Ronno Das, Brian Lehmann, and Philip Tosteson.
There have been extensive activities on counting functions of rational points of bounded height on del Pezzo surfaces, and one of prominent approaches to this problem is by the usage of conic bundle structures on del Pezzo surfaces. This leads to upper and lower bounds of correct magnitude for quartic del Pezzo surfaces.
In this talk, I will explain how conic bundle structures on del Pezzo surfaces induce fibration structures on the spaces of rational curves on such surfaces. Then I will explain applications of this structure which include:
1. upper bounds of correct magnitude for the counting function of rational curves on quartic del Pezzo surfaces over finite fields.
2. rationality of the space of rational curves on a quartic del Pezzo surface.
Finally, I will explain our ongoing proof of homological stability for the spaces of rational curves on quartic del Pezzo surfaces. This is joint work in progress with Ronno Das, Brian Lehmann, and Philip Tosteson.
