TY - JOUR
T1 - Fundamental groups of galois closures of generic projections
AU - Liedtke, Christian
PY - 2010/4
Y1 - 2010/4
N2 - For the Galois closure Xgal of a generic projection from a surface X, it is believed that pi;1(Xgal) gives rise to new invariants of X. However, in all examples this group is surprisingly simple. In this article, we offer an explanation for this phenomenon: We compute a quotient of π1(Xgal)that depends on π1(X) and data from the generic projection only. In all known examples, this quotient is in fact isomorphic to π1(Xgal). As a byproduct, we simplify the computations of Moishezon, Teicher and others.
AB - For the Galois closure Xgal of a generic projection from a surface X, it is believed that pi;1(Xgal) gives rise to new invariants of X. However, in all examples this group is surprisingly simple. In this article, we offer an explanation for this phenomenon: We compute a quotient of π1(Xgal)that depends on π1(X) and data from the generic projection only. In all known examples, this quotient is in fact isomorphic to π1(Xgal). As a byproduct, we simplify the computations of Moishezon, Teicher and others.
UR - http://www.scopus.com/inward/record.url?scp=77950900514&partnerID=8YFLogxK
U2 - 10.1090/S0002-9947-09-04941-1
DO - 10.1090/S0002-9947-09-04941-1
M3 - Article
AN - SCOPUS:77950900514
SN - 0002-9947
VL - 362
SP - 2167
EP - 2188
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
IS - 4
ER -