S. S. Chern, F. Hirzebruch, and J.-P. Serre :
“On the index of a fibered manifold Proc. Am. Math. Soc.
8 : 3
(1957 ),
pp. 587–596 .
MR
87943 Zbl
0083.17801 article
People
BibTeX
@article {key87943m,
AUTHOR = {Chern, S. S. and Hirzebruch, F. and
Serre, J.-P.},
TITLE = {On the index of a fibered manifold},
JOURNAL = {Proc. Am. Math. Soc.},
FJOURNAL = {Proceedings of the American Mathematical
Society},
VOLUME = {8},
NUMBER = {3},
YEAR = {1957},
PAGES = {587--596},
DOI = {10.2307/2033523},
NOTE = {MR:87943. Zbl:0083.17801.},
ISSN = {0002-9939},
}
F. Hirzebruch :
“The canonical map for certain Hilbert modular surfaces 75–95
in
The Chern symposium 1979
(Berkeley, CA, June 1979 ).
Edited by W.-Y. Hsiang, S. Kobayashi, I. M. Singer, J. Wolf, H.-H. Wu, and A. Weinstein .
Springer (New York ),
1980 .
MR
609558 Zbl
0457.14019 incollection
Abstract
People
BibTeX
It was a real pleasure for me to participate in the symposium in honor of Shiing-shen Chern. In my lecture I intended to give a survey on Hilbert modular surfaces. But actually I discussed examples of such Hilbert modular surfaces for which specific information is available on their structure as algebraic surfaces. The paper presented here is an extended version of the talk.
Algebraic surfaces are often investigated by means of their pluricanonical maps (see for example Bombieri [1973]). The properties of the canonical map itself (given by the secctions of the canonical bundle or in the case of Hilbert modular surfaces by the cusp forms of weight 2) are relatively complicated (compare Beauville [1979]). In a certain range, namely for minimal surfaces of general type with
\[ 2p_g - 4 \leq K^2 \leq 2p_g - 2 ,\]
Horikawa’s results are available [1975, 1976a, 1976b, 1978, 1979]. To apply them, one has to prove that the surface being studied is minimal. For Hilbert modular surfaces this is a difficult problem, which was attacked first by van der Geer and Van de Ven [1977]. Van der Geer has obtained many results on the structure of special Hilbert modular surfaces [1978, 1979] including some of the surfaces studied here.
The rough classification of Hilbert modular surfaces according to rational, \( K3 \) , elliptic, and general type was considered in [Hirzebruch and Van de Ven 1974; Hirzebruch and Zagier 1977; Hirzebruch 1978]. The present paper tries to show that in some cases a finer classification of the surfaces of general type can be obtained.
@incollection {key609558m,
AUTHOR = {Hirzebruch, F.},
TITLE = {The canonical map for certain {H}ilbert
modular surfaces},
BOOKTITLE = {The {C}hern symposium 1979},
EDITOR = {Hsiang, W.-Y. and Kobayashi, S. and
Singer, I. M. and Wolf, J. and Wu, H.-H.
and Weinstein, A.},
PUBLISHER = {Springer},
ADDRESS = {New York},
YEAR = {1980},
PAGES = {75--95},
DOI = {10.1007/978-1-4613-8109-9_5},
NOTE = {(Berkeley, CA, June 1979). MR:609558.
Zbl:0457.14019.},
ISBN = {9781461381112},
}
Wolf prize in mathematics ,
vol. 1 .
Edited by S. S. Chern and F. Hirzebruch .
World Scientific (River Edge, NJ ),
2000 .
MR
1834907 Zbl
0972.01032 book
People
BibTeX
@book {key1834907m,
TITLE = {Wolf prize in mathematics},
EDITOR = {Chern, S. S. and Hirzebruch, F.},
VOLUME = {1},
PUBLISHER = {World Scientific},
ADDRESS = {River Edge, NJ},
YEAR = {2000},
PAGES = {xii+761},
NOTE = {MR:1834907. Zbl:0972.01032.},
ISBN = {9789810239459},
}
F. Hirzebruch :
“Response for Lars Hörmander and Friederich Hirzebruch ,”
pp. 389
in
Wolf Prize in Mathematics ,
vol. 1 .
Edited by S. S. Chern and F. Hirzebruch .
World Scientific (River Edge, NJ ),
2000 .
Wolf Prize Ceremony, The Knesset, Jerusalem, May 12, 1988.
incollection
People
BibTeX
@incollection {key72183275,
AUTHOR = {Hirzebruch, Friederich},
TITLE = {Response for {L}ars {H}\"ormander and
{F}riederich {H}irzebruch},
BOOKTITLE = {Wolf Prize in Mathematics},
EDITOR = {Chern, S. S. and Hirzebruch, F.},
VOLUME = {1},
PUBLISHER = {World Scientific},
ADDRESS = {River Edge, NJ},
YEAR = {2000},
PAGES = {389},
NOTE = {Wolf Prize Ceremony, The Knesset, Jerusalem,
May 12, 1988.},
ISBN = {9789810239466},
}
Wolf prize in mathematics ,
vol. 2 .
Edited by S. S. Chern and F. Hirzebruch .
World Scientific (River Edge, NJ ),
2001 .
MR
1863749 Zbl
1030.01001 book
People
BibTeX
@book {key1863749m,
TITLE = {Wolf prize in mathematics},
EDITOR = {Chern, S. S. and Hirzebruch, F.},
VOLUME = {2},
PUBLISHER = {World Scientific},
ADDRESS = {River Edge, NJ},
YEAR = {2001},
PAGES = {xiii+918},
NOTE = {MR:1863749. Zbl:1030.01001.},
ISBN = {9789810239466},
}
F. Hirzebruch and U. Simon :
“Nachruf auf Shiing-Shen Chern ”
[Obituary for Shiing-Shen Chern ],
Jahresber. Dtsch. Math.-Ver.
108 : 4
(2006 ),
pp. 197–217 .
MR
2287091 Zbl
1156.01340 article
People
BibTeX
@article {key2287091m,
AUTHOR = {Hirzebruch, Friedrich and Simon, Udo},
TITLE = {Nachruf auf {S}hiing-{S}hen {C}hern
[Obituary for {S}hiing-{S}hen {C}hern]},
JOURNAL = {Jahresber. Dtsch. Math.-Ver.},
FJOURNAL = {Jahresbericht der Deutschen Mathematiker-Vereinigung},
VOLUME = {108},
NUMBER = {4},
YEAR = {2006},
PAGES = {197--217},
NOTE = {MR:2287091. Zbl:1156.01340.},
ISSN = {0012-0456},
CODEN = {JDMVA7},
}
S.-T. Yau, F. E. P. Hirzebruch, M. Atiyah, M. do Carmo, R. E. Greene, W.-l. Huang, K. Reich, L. Ji, J. Li, E. Kuh, Y. R. Shen, I. M. Singer, A. Weinstein, and J. A. Wolf :
“Shiing-Shen Chern (1911–2004) Notices Am. Math. Soc.
58 : 9
(October 2011 ),
pp. 1226–1249 .
Hirzebruch’s contribution to this article was also published in Frontiers of mathematical sciences (2011)
MR
2868099 Zbl
1228.01052 article
People
BibTeX
@article {key2868099m,
AUTHOR = {Yau, Shing-Tung and Hirzebruch, Friedrich
Ernst Peter and Atiyah, Michael and
do Carmo, Manfredo and Greene, Robert
E. and Huang, Wen-ling and Reich, Karin
and Ji, Lizhen and Li, Jun and Kuh,
Ernest and Shen, Y. Ron and Singer,
Isadore M. and Weinstein, Alan and Wolf,
Joseph A.},
TITLE = {Shiing-{S}hen {C}hern (1911--2004)},
JOURNAL = {Notices Am. Math. Soc.},
FJOURNAL = {Notices of the American Mathematical
Society},
VOLUME = {58},
NUMBER = {9},
MONTH = {October},
YEAR = {2011},
PAGES = {1226--1249},
URL = {http://www.ams.org/notices/201109/rtx110901226p.pdf},
NOTE = {Hirzebruch's contribution to this article
was also published in \textit{Frontiers
of mathematical sciences} (2011). MR:2868099.
Zbl:1228.01052.},
ISSN = {0002-9920},
}
F. Hirzebruch :
“Why do I like Chern? And why do I like Chern classes? ,”
pp. 61–67
in
Frontiers of mathematical sciences: The inauguration of the Mathematical Sciences Center of Tsinghua University and the Tsinghua-Sanya International Mathematics Forum .
Edited by B. Gu and S.-T. Yau .
International Press (Somerville, MA ),
2011 .
This was included as Hirzebruch’s contribution to a multi-author obituary for Chern in Notices Am. Math. Soc. 58 :9 (2011)
MR
3050817 incollection
People
BibTeX
@incollection {key3050817m,
AUTHOR = {Hirzebruch, Friedrich},
TITLE = {Why do {I} like {C}hern? {A}nd why do
{I} like {C}hern classes?},
BOOKTITLE = {Frontiers of mathematical sciences:
{T}he inauguration of the {M}athematical
{S}ciences {C}enter of {T}singhua {U}niversity
and the {T}singhua-{S}anya {I}nternational
{M}athematics {F}orum},
EDITOR = {Gu, Binglin and Yau, Shing-Tung},
PUBLISHER = {International Press},
ADDRESS = {Somerville, MA},
YEAR = {2011},
PAGES = {61--67},
NOTE = {This was included as Hirzebruch's contribution
to a multi-author obituary for Chern
in \textit{Notices Am. Math. Soc.} \textbf{58}:9
(2011). MR:3050817.},
ISBN = {9781571461230},
}
