论文标题

Manin-pehre的猜想,用于光滑球形三倍

The Manin-Peyre conjecture for smooth spherical Fano threefolds

论文作者

Blomer, Valentin, Brüdern, Jörg, Derenthal, Ulrich, Gagliardi, Giuliano

论文摘要

建立了Manin-pehre的猜想,用于平滑球形球形三倍的半神经等级。案例n具有许多结构性新颖性;最值得注意的是,一个人可能会失去环境复合物品种的规律性,高度条件可能包含分数指数,并且可能有必要排除一个薄的子集,而从计数中出现了非常多的理性点,否则,否则Manin以其原始形式的猜想将不正确。

The Manin-Peyre conjecture is established for smooth spherical Fano threefolds of semisimple rank one and type N. Together with the previously solved case T and the toric cases, this covers all types of smooth spherical Fano threefolds. The case N features a number of structural novelties; most notably, one may lose regularity of the ambient toric variety, the height conditions may contain fractional exponents, and it may be necessary to exclude a thin subset with exceptionally many rational points from the count, as otherwise Manin's conjecture in its original form would turn out to be incorrect.

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