TY - JOUR

T1 - THE FUNDAMENTAL GROUP OF THE GALOIS COVER OF HIRZEBRUCH SURFACE F1(2, 2)

AU - MEIRAV, AMRAM

AU - Teicher, M.

AU - UZI, VISHNE

PY - 2007

Y1 - 2007

N2 - This paper is the second in a series of papers concerning Hirzebruch surfaces. In the first paper in this series, the fundamental group of Galois covers of Hirzebruch surfaces Fk(a, b), where a, b are relatively prime, was shown to be trivial. For the general case, the conjecture stated that the fundamental group is where c = gcd(a, b) and n = 2ab + kb2. In this paper, we degenerate the Hirzebruch surface F1(2, 2), compute the braid monodromy factorization of the branch curve in ℂ2, and verify that, in this case, the conjecture holds: the fundamental group of the Galois cover of F1(2, 2) with respect to a generic projection is isomorphic to .
Read More: http://www.worldscientific.com/doi/abs/10.1142/S0218196707003780

AB - This paper is the second in a series of papers concerning Hirzebruch surfaces. In the first paper in this series, the fundamental group of Galois covers of Hirzebruch surfaces Fk(a, b), where a, b are relatively prime, was shown to be trivial. For the general case, the conjecture stated that the fundamental group is where c = gcd(a, b) and n = 2ab + kb2. In this paper, we degenerate the Hirzebruch surface F1(2, 2), compute the braid monodromy factorization of the branch curve in ℂ2, and verify that, in this case, the conjecture holds: the fundamental group of the Galois cover of F1(2, 2) with respect to a generic projection is isomorphic to .
Read More: http://www.worldscientific.com/doi/abs/10.1142/S0218196707003780

UR - http://www.worldscientific.com/doi/abs/10.1142/S0218196707003780

M3 - Article

SN - 0218-1967

VL - 17

SP - 507

EP - 525

JO - International Journal of Algebra and Computation

JF - International Journal of Algebra and Computation

IS - 3

ER -