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代数幾何学セミナー
過去の記録 ～06/14｜次回の予定｜今後の予定 06/15～
| 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 |
2025年06月20日(金)
13:30-15:00 数理科学研究科棟(駒場) 118号室
岡村 郁弥 氏 (中央大学)
Moduli spaces of rational curves on Artin-Mumford double solids
岡村 郁弥 氏 (中央大学)
Moduli spaces of rational curves on Artin-Mumford double solids
[ 講演概要 ]
Artin-Mumford double solids were originally constructed as examples of unirational but irrational varieties. Their method showed that the Brauer group gives an obstruction to rationality. Later, Voisin observed that this obstruction measures the difference between algebraic and numerical equivalence for 1-cycles.
In this talk, we study the moduli spaces of rational curves on Artin-Mumford double solids. First, we discuss the relation between the spaces of lines on these varieties and certain Enriques surfaces known as Reye congruences. Then, we classify all irreducible components of the moduli spaces of rational curves of each degree, and prove Geometric Manin's Conjecture in this setting.
Artin-Mumford double solids were originally constructed as examples of unirational but irrational varieties. Their method showed that the Brauer group gives an obstruction to rationality. Later, Voisin observed that this obstruction measures the difference between algebraic and numerical equivalence for 1-cycles.
In this talk, we study the moduli spaces of rational curves on Artin-Mumford double solids. First, we discuss the relation between the spaces of lines on these varieties and certain Enriques surfaces known as Reye congruences. Then, we classify all irreducible components of the moduli spaces of rational curves of each degree, and prove Geometric Manin's Conjecture in this setting.
