论文标题
形态方案和对爆破的应用的特性
Properties of schemes of morphisms and applications to blow-ups
论文作者
论文摘要
令$ x $为固定的投影方案，在基本方案$ s $上是固定的。该协会将准标准$ s $ -scheme $ y $ $ y $ $ y $用于参数化$ s $ s $ - 米代表从$ x $到$ y $。我们证明该函子可以保留限制，并且既开放又封闭的沉浸式。作为应用程序，我们确定了在有限的许多点上对射击空间的爆炸进行参数化有理曲线的分区。我们计算其组件的尺寸，其中包含特殊除数之外的有理曲线以及严格包含在其中的曲线。此外，我们为适当相交的不可约组件的尺寸提供了上限。
Let $X$ be a fixed projective scheme which is flat over a base scheme $S$. The association taking a quasi-projective $S$-scheme $Y$ to the scheme parametrizing $S$-morphisms from $X$ to $Y$ is functorial. We prove that this functor preserves limits, and both open and closed immersions. As an application, we determine a partition of schemes parametrizing rational curves on the blow-ups of projective spaces at finitely many points. We compute the dimensions of its components containing rational curves outside the exceptional divisor and the ones strictly contained in it. Furthermore, we provide an upper bound for the dimension of the irreducible components intersecting the exceptional divisors properly.
