论文标题
用非多聚体有效锥体吹动的曲折表面
Blown-up toric surfaces with non-polyhedral effective cone
论文作者
论文摘要
我们构建了投射曲折表面的例子，它们在一般点的爆炸具有非多层伪有效的锥体，无论是特征性$ 0 $还是在每个主要特征$ p $中。结果，我们证明了Grothendieck-Knudsen Moduli Space的伪有效锥体$ \ overline m_ {0，n} $稳定的理性曲线并不是$ n \ geq 10 $的特征性$ 0 $的$ n \ geq 10 $的特征性$ p $，并且对于所有普rimes $ p $，primes $ p $ p $ p $。这些复曲面的许多表面与非常有趣的算术三倍有关，我们称之为无限顺序的算术椭圆对。他们在特征性$ p $中的分析依靠算术几何形状和Galois表示的工具，本着Lang-Trotter的猜想的精神产生折叠表面，它们的爆炸在一般角度具有非多伪伪有效的锥体，其特征性$ 0 $，并且在特征性的$ p $中，对于无限的Prime $ $ $ $ P $ $ P $。
We construct examples of projective toric surfaces whose blow-up at a general point has a non-polyhedral pseudo-effective cone, both in characteristic $0$ and in every prime characteristic $p$. As a consequence, we prove that the pseudo-effective cone of the Grothendieck-Knudsen moduli space $\overline M_{0,n}$ of stable rational curves is not polyhedral for $n\geq 10$ in characteristic $0$ and in characteristic $p$, for all primes $p$. Many of these toric surfaces are related to a very interesting class of arithmetic threefolds that we call arithmetic elliptic pairs of infinite order. Their analysis in characteristic $p$ relies on tools of arithmetic geometry and Galois representations in the spirit of the Lang-Trotter conjecture, producing toric surfaces whose blow-up at a general point has a non-polyhedral pseudo-effective cone in characteristic $0$ and in characteristic $p$, for an infinite set of primes $p$ of positive density.
