| 释义 |
- References
In mathematics, a Kodaira surface is a compact complex surface of Kodaira dimension 0 and odd first Betti number. These are never algebraic, though they have non-constant meromorphic functions. They are usually divided into two subtypes: primary Kodaira surfaces with trivial canonical bundle, and secondary Kodaira surfaces which are quotients of these by finite groups of orders 2, 3, 4, or 6, and which have non-trivial canonical bundles. The secondary Kodaira surfaces have the same relation to primary ones that Enriques surfaces have to K3 surfaces, or bielliptic surfaces have to abelian surfaces. Invariants: If the surface is the quotient of a primary Kodaira surface by a group of order k=1,2,3,4,6, then the plurigenera Pn are 1 if n is divisible by k and 0 otherwise. Hodge diamond:{{Hodge diamond|style=font-weight:bold
| 1
| 1 | 2
| 1 | 2 | 1 | note = (Primary)
| 2 | 1
| 1
}}{{Hodge diamond|style=font-weight:bold
| 1
| 0 | 1
| 0 | 0 | 0 | note = (Secondary)
| 1 | 0
| 1
}}Examples: Take a non-trivial line bundle over an elliptic curve, remove the zero section, then quotient out the fibers by Z acting as multiplication by powers of some complex number z. This gives a primary Kodaira surface. References- {{Citation | last1=Barth | first1=Wolf P. | last2=Hulek | first2=Klaus | last3=Peters | first3=Chris A.M. | last4=Van de Ven | first4=Antonius | title=Compact Complex Surfaces | publisher= Springer-Verlag, Berlin | series=Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. | isbn=978-3-540-00832-3 | mr=2030225 | year=2004 | volume=4}} – the standard reference book for compact complex surfaces
- {{Citation | last1=Kodaira | first1=Kunihiko | title=On the structure of compact complex analytic surfaces. I | jstor=2373157 | mr=0187255 | year=1964 | journal=American Journal of Mathematics | issn=0002-9327 | volume=86 | issue=4 | pages=751–798 | doi=10.2307/2373157}}
- {{Citation | last1=Kodaira | first1=Kunihiko | title=On the structure of compact complex analytic surfaces. II | jstor=2373150 | mr=0205280 | year=1966 | journal=American Journal of Mathematics | issn=0002-9327 | volume=88 | issue=3 | pages=682–721 | doi=10.2307/2373150| pmc=300219 }}
- {{Citation | last1=Kodaira | first1=Kunihiko | title=On the structure of compact complex analytic surfaces. III | jstor=2373426 | mr=0228019 | year=1968 | journal=American Journal of Mathematics | issn=0002-9327 | volume=90 | issue=1 | pages=55–83 | doi=10.2307/2373426| pmc=300219 }}
- {{Citation | last1=Kodaira | first1=Kunihiko | title=On the structure of complex analytic surfaces. IV | jstor=2373289 | mr=0239114 | year=1968 | journal=American Journal of Mathematics | issn=0002-9327 | volume=90 | issue=4 | pages=1048–1066 | doi=10.2307/2373289}}
1 : Complex surfaces |