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Moduli spaces and braid monodromy types of bidouble covers of the quadric

Title data

Catanese, Fabrizio ; Lönne, Michael ; Wajnryb, Bronislaw:
Moduli spaces and braid monodromy types of bidouble covers of the quadric.
In: Geometry & Topology. Vol. 15 (2011) Issue 1 . - pp. 351-396.
ISSN 1364-0380
DOI: https://doi.org/10.2140/gt.2011.15.351

Abstract in another language

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.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: braid momodromy factorization; surfaces of general type
Subject classification: Mathematics Subject Classification Code: 14D05 14J29
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Former Professors > Professorship Algebraic Geometry - apl. Prof. Dr. Michael Lönne
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 23 Nov 2021 13:55
Last Modified: 23 Nov 2021 14:36
URI: https://eref.uni-bayreuth.de/id/eprint/67988