Details
| Original language | English |
|---|---|
| Pages (from-to) | 351-396 |
| Number of pages | 46 |
| Journal | Geometry and Topology |
| Volume | 15 |
| Issue number | 1 |
| Publication status | Published - 2011 |
| Externally published | Yes |
Abstract
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In: Geometry and Topology, Vol. 15, No. 1, 2011, p. 351-396.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Moduli spaces and braid monodromy types of bidouble covers of the quadric
AU - Catanese, Fabrizio
AU - Lönne, Michael
AU - Wajnryb, Bronislaw
PY - 2011
Y1 - 2011
N2 - 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 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 o 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.
AB - 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 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 o 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.
UR - http://www.scopus.com/inward/record.url?scp=79952970072&partnerID=8YFLogxK
UR - http://arxiv.org/abs/0910.2142
U2 - 10.2140/gt.2011.15.351
DO - 10.2140/gt.2011.15.351
M3 - Article
AN - SCOPUS:79952970072
VL - 15
SP - 351
EP - 396
JO - Geometry and Topology
JF - Geometry and Topology
SN - 1364-0380
IS - 1
ER -