1999 Fiscal Year Final Research Report Summary
STUDY ON THE COMPLEX AFFINE SPACE CィイD1NィエD1 AND ITS COMPACTIFICATION
| Project/Area Number |
10640026
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | KUMAMOTO UNIVERSITY (1999)
Hiroshima University (1998) |
|---|
Principal Investigator |
FURUSHIMA Mikio KUMAMOTO UNIVERSITY, FACULTY OF SCIENCE, PROFESSOR, 理学部, 教授 (00165482)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
ABE Makoto OSHIMA NATIONAL COLLEGE OF MARITIME TECHNOLOGY, ASSOCIATED PROFESSOR, 一般科, 助教授 (90159442)
|
|---|
| Project Period (FY) |
1998 – 1999
|
| Keywords | COMPLEX AFFINE SPACES / COMPACTIFICATION / MOISHEZON |
|---|
| Research Abstract |
We investigated projective compactifications or non-projective Moishezon compactifications of CィイD13ィエD1 and the classification of minimal normal compactifications of CィイD12ィエD1/G, where G is a small finite subgroup of the general linear group GL(2,C), and we obtained several new results. We will state as follows. There are six types of projective compactifications of CィイD13ィエD1 with second Betti number equal to one. This was obtained by Furushima before. In this research, we gave a concrete construction of these six compactifications of C3 from the well-known compactifications (PィイD13ィエD1,PィイD12ィエD1), that is, we gave an explicit birational map of PィイD13ィエD1 to X which is biregular on CィイD13ィエD1-part. This finishes the projective classifications of such compactifications of CィイD13ィエD1.
Next, we also studied the structure of the non-projective compactifications (X,Y) of CィイD13ィエD1 with second Betti number equal to one. In this case, it is easy to see that the canonical divisor can be written as follow: KX=-rY (r>0 is an integer). In this research, we can show that the integer r is equal to one or two and that there are many new examples of such non-projective compactifications of CィイD13ィエD1.
Furthermore, we find that some technique developed in the study of compactifications of CィイD13ィエD1 can be applied to the classification of the minimal normal compactifications of CィイD12ィエD1/G, then we succeeded in its classification.
|
