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Catanese, Fabrizio ; Lönne, Michael ; Wajnryb, Bronislaw:
Moduli spaces and braid monodromy types of bidouble covers of the quadric.
In: Geometry & Topology.
Bd. 15
(2011)
Heft 1
.
- S. 351-396.
ISSN 1364-0380
DOI: https://doi.org/10.2140/gt.2011.15.351
Abstract
Bidouble covers π:S→Q:=P1×P1 of the quadric are parametrized by connected families depending on four positive integers a,b,c,d. In the special case where b=d we call them abc–surfaces.
Such a Galois covering π admits a small perturbation yielding a general 4–tuple covering of Q with branch curve Δ, and a natural Lefschetz fibration obtained from a small perturbation of the composition p1∘π.
We prove a more general result implying that the braid monodromy factorization corresponding to Δ determines the three integers a,b,c in the case of abc–surfaces. We introduce a new method in order to distinguish factorizations which are not stably equivalent.
This result is in sharp contrast with a previous result of the first and third author, showing that the mapping class group factorizations corresponding to the respective natural Lefschetz pencils are equivalent for abc–surfaces with the same values of a+c,b. This result hints at the possibility that abc–surfaces with fixed values of a+c,b, although diffeomorphic but not deformation equivalent, might be not canonically symplectomorphic.
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| Publikationsform: | Artikel in einer Zeitschrift |
|---|---|
| Begutachteter Beitrag: | Ja |
| Keywords: | braid momodromy factorization; surfaces of general type |
| Fachklassifikationen: | Mathematics Subject Classification Code: 14D05 14J29 |
| Institutionen der Universität: | Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut > Ehemalige Professoren > Professur Algebraische Geometrie - apl. Prof. Dr. Michael Lönne Fakultäten Fakultäten > Fakultät für Mathematik, Physik und Informatik Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut > Ehemalige Professoren |
| Titel an der UBT entstanden: | Ja |
| Themengebiete aus DDC: | 500 Naturwissenschaften und Mathematik > 510 Mathematik |
| Eingestellt am: | 23 Nov 2021 13:55 |
| Letzte Änderung: | 23 Nov 2021 14:36 |
| URI: | https://eref.uni-bayreuth.de/id/eprint/67988 |