Comptes Rendus
Article de recherche - Analyse et géométrie complexes
Irregularity of some toroidal compactifications
[Irrégularité de certaines compactifications toroïdales]
Comptes Rendus. Mathématique, Volume 364 (2026), pp. 199-204

We compute the irregularity of certain $2$-dimensional toroidal compactifications.

Nous calculons l’irrégularité de certaines compactifications toroïdales en dimension $2$.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/crmath.794
Classification : 14J29, 14F17, 51M10
Keywords: Toroidal compactification, irregularity, Kähler hyperbolicity
Mots-clés : Compactification toroïdale, irrégularité, hyperbolicité de Kähler

Ilya Karzhemanov  1

1 Moscow Institute of Physics and Technology, 9 Institutskiy per., Dolgoprudny, Moscow Region, 141701, Russia
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
@article{CRMATH_2026__364_G1_199_0,
     author = {Ilya Karzhemanov},
     title = {Irregularity of some toroidal compactifications},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {199--204},
     year = {2026},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {364},
     doi = {10.5802/crmath.794},
     language = {en},
}
TY  - JOUR
AU  - Ilya Karzhemanov
TI  - Irregularity of some toroidal compactifications
JO  - Comptes Rendus. Mathématique
PY  - 2026
SP  - 199
EP  - 204
VL  - 364
PB  - Académie des sciences, Paris
DO  - 10.5802/crmath.794
LA  - en
ID  - CRMATH_2026__364_G1_199_0
ER  - 
%0 Journal Article
%A Ilya Karzhemanov
%T Irregularity of some toroidal compactifications
%J Comptes Rendus. Mathématique
%D 2026
%P 199-204
%V 364
%I Académie des sciences, Paris
%R 10.5802/crmath.794
%G en
%F CRMATH_2026__364_G1_199_0
Ilya Karzhemanov. Irregularity of some toroidal compactifications. Comptes Rendus. Mathématique, Volume 364 (2026), pp. 199-204. doi: 10.5802/crmath.794

[1] Ian Agol Virtual Betti numbers of symmetric spaces (2006) | arXiv | Zbl

[2] Luca F. Di Cerbo; Matthew Stover Bielliptic ball quotient compactifications and lattices in PU(2,1) with finitely generated commutator subgroup, Ann. Inst. Fourier, Volume 67 (2017) no. 1, pp. 315-328 | DOI | MR | Zbl

[3] Mikhael Gromov Kähler hyperbolicity and L 2 -Hodge theory, J. Differ. Geom., Volume 33 (1991) no. 1, pp. 263-292 | MR | Zbl

[4] Friedrich Ernst Peter Hirzebruch Arrangements of lines and algebraic surfaces, Arithmetic and geometry, Vol. II (Michael Artin; John Tate, eds.) (Progress in Mathematics), Volume 36, Birkhäuser, 1983, pp. 113-140 | MR | DOI | Zbl

[5] Friedrich Ernst Peter Hirzebruch Chern numbers of algebraic surfaces: an example, Math. Ann., Volume 266 (1984) no. 3, pp. 351-356 | DOI | MR | Zbl

[6] Rolf-Peter Holzapfel Chern numbers of algebraic surfaces — Hirzebruch’s examples are Picard modular surfaces, Math. Nachr., Volume 126 (1986), pp. 255-273 | DOI | MR | Zbl

[7] Rolf-Peter Holzapfel Ball and surface arithmetics, Aspects of Mathematics, E29, Vieweg & Sohn, 1998 | DOI | MR | Zbl

[8] Masa-Nori Ishida The irregularities of Hirzebruch’s examples of surfaces of general type with c 1 2 =3c 2 , Math. Ann., Volume 262 (1983) no. 3, pp. 407-420 | DOI | MR | Zbl

[9] Azniv K. Kasparian; Gregory Kumar Sankaran Fundamental groups of toroidal compactifications, Asian J. Math., Volume 22 (2018) no. 5, pp. 941-953 | DOI | MR | Zbl

[10] János Kollár Shafarevich maps and automorphic forms, M. B. Porter Lectures, Princeton University Press, 1995 | DOI | MR | Zbl

[11] H. Blaine Lawson; Shing Tung Yau Compact manifolds of nonpositive curvature, J. Differ. Geom., Volume 7 (1972), pp. 211-228 | MR | Zbl

[12] Aleksander Momot Irregular ball-quotient surfaces with non-positive Kodaira dimension, Math. Res. Lett., Volume 15 (2008) no. 6, pp. 1187-1195 | DOI | MR | Zbl

[13] David Bryant Mumford Hirzebruch’s proportionality theorem in the noncompact case, Invent. Math., Volume 42 (1977), pp. 239-272 | DOI | MR | Zbl

[14] Matthew Stover Cusp and b 1 growth for ball quotients and maps onto with finitely generated kernel, Indiana Univ. Math. J., Volume 70 (2021) no. 1, pp. 213-233 | DOI | MR | Zbl

[15] Kang Zuo Kummer-Überlagerungen algebraischer Flächen, Bonner Mathematische Schriften, 193, Mathematisches Institut der Universität Bonn, 1989 | MR | Zbl

Cité par Sources :

Commentaires - Politique