TY - JOUR

T1 - On non fundamental group equivalent surfaces

AU - Teicher, Mina

AU - Friedman, Michael

PY - 2008

Y1 - 2008

N2 - In this paper we present an example of two polarized K3 surfaces which are not Fundamental Group Equivalent (their fundamental groups of the complement of the branch curves are not isomorphic; denoted by FGE) but the fundamental groups of their related Galois covers are isomorphic. For each surface, we consider a generic projection to CP2 and a degenerations of the surface into a union of planes - the "pillow" degeneration for the non prime surface and the "magician" degeneration for the prime surface. We compute the Braid Monodromy Factorization (BMF) of the branch curve of each projected surface, using the related degenerations. By these factorizations, we compute the above fundamental groups. It is known that the two surfaces are not in the same component of the Hilbert scheme of linearly embedded K3 surfaces. Here we prove that furthermore they are not FGE equivalent, and thus they are not of the same Braid Monodromy Type (BMT) (which implies that they are not a projective deformation of each other).

AB - In this paper we present an example of two polarized K3 surfaces which are not Fundamental Group Equivalent (their fundamental groups of the complement of the branch curves are not isomorphic; denoted by FGE) but the fundamental groups of their related Galois covers are isomorphic. For each surface, we consider a generic projection to CP2 and a degenerations of the surface into a union of planes - the "pillow" degeneration for the non prime surface and the "magician" degeneration for the prime surface. We compute the Braid Monodromy Factorization (BMF) of the branch curve of each projected surface, using the related degenerations. By these factorizations, we compute the above fundamental groups. It is known that the two surfaces are not in the same component of the Hilbert scheme of linearly embedded K3 surfaces. Here we prove that furthermore they are not FGE equivalent, and thus they are not of the same Braid Monodromy Type (BMT) (which implies that they are not a projective deformation of each other).

KW - Branch curve

KW - Curves and singularities

KW - Fundamental group

KW - Generic projection

UR - http://www.scopus.com/inward/record.url?scp=72949104945&partnerID=8YFLogxK

U2 - 10.2140/agt.2008.8.397

DO - 10.2140/agt.2008.8.397

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:72949104945

SN - 1472-2747

VL - 8

SP - 397

EP - 433

JO - Algebraic and Geometric Topology

JF - Algebraic and Geometric Topology

IS - 1

ER -