Moduli Space of Polarized del Pezzo Surfaces and its Compactification
Moduli Space of Polarized del Pezzo Surfaces and its Compactification
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偏振del Pezzo曲面的模空间及其紧致化
DOI：
10.3836/tjm/1270214895
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发表时间：
1982
影响因子：
0.6
通讯作者：
S. Ishii
中科院分区：
文献类型：
--
作者：
S. Ishii
$\omega_{X}^{-1}=d$。已知当$d=9时，del Pezzo曲面的次数至多为9，且当$d=9时，它同构于$P^{2}$，当$d=8$时，$$P^{1}同构于$P^{1}$或$F_{1}$，当$d=8$时，在中心为$(9-d)$-闭点的么正变换下，$P^{2}$的像是同构的。定义1)如果$1\leqq d\leqq 7$([2])。设$X$是7次Del Pezzo曲面，$f：x\right tarrow P^{2}$是中心$(9-d)$点在一般位置的单线变换。我们称$f^{*}P_{P^{2}}(1)$为$X上的收缩层。本文首先构造了Del Pezzo曲面的模空间和压缩层，然后在定义7的意义下构造了它的紧化.在S 1中，我们实现了Del Pezzo曲面模空间
$\omega_{X}^{-1}=d$ . It is known that the degree of a del Pezzo surface is at most 9 and the surface is isomorphic to $P^{2}$ if $d=9,$ $P^{1}\times P^{1}$ or $F_{1}$ if $d=8$ , the image of $P^{2}$ under a monoidal transformation with center $(9-d)$-closed points in general position (cf. Definition 1) if $1\leqq d\leqq 7$ ([2]). Let $X$ be a del Pezzo surface of degree $d\leqq 7$ and $f:X\rightarrow P^{2}$ be a monoidal transformation of $P^{2}$ with center $(9-d)$-points in general position. We call the sheaf $f^{*}P_{P^{2}}(1)$ a contraction sheaf on $X$. In this article we first construct the moduli space of del Pezzo surfaces of degree $d(1\leqq d\leqq 7)$ together with a contraction sheaf, and next construct its compactification in the sense of Definition 7. In \S 1, we realize the moduli space of del Pezzo surfaces of degree