TY - JOUR

T1 - The regeneration of a 5-point

AU - Friedman, Michael

AU - Teicher, Mina

PY - 2008

Y1 - 2008

N2 - The braid monodromy factorization of the branch curve of a surface of general type is known to be an invariant that completely determines the diffeomorphism type of the surface (see [2]). Calculating this factorization is of high technical complexity; computing the braid monodromy factorization of branch curves of surfaces uncovers new facts and invariants of the surfaces. Since finding the branch curve of a surface is very difficult, we degenerate the surface into a union of planes. Thus, we can find the braid monodromy of the branch curve of the degenerated surface, which is a union of lines. The regeneration of the singularities of the branch curve, studied locally, leads us to find the global braid monodromy factorization of the branch curve of the original surface. So far, only the regeneration of the BMF of 3,4 and 6-point (a singular point which is the intersection of 3 / 4 / 6 planes; see [6],[8]) were done. In this paper, we fill the gap and find the braid monodromy of the regeneration of a 5-point. This is of great importance to the understanding of the BMT (braid monodromy type) of surfaces [2]. This braid monodromy will be used to find the global braid monodromy factorization of different surfaces; in particular - the monodromy of the branch curve of the Hirzebruch surface F2,(2,2).

AB - The braid monodromy factorization of the branch curve of a surface of general type is known to be an invariant that completely determines the diffeomorphism type of the surface (see [2]). Calculating this factorization is of high technical complexity; computing the braid monodromy factorization of branch curves of surfaces uncovers new facts and invariants of the surfaces. Since finding the branch curve of a surface is very difficult, we degenerate the surface into a union of planes. Thus, we can find the braid monodromy of the branch curve of the degenerated surface, which is a union of lines. The regeneration of the singularities of the branch curve, studied locally, leads us to find the global braid monodromy factorization of the branch curve of the original surface. So far, only the regeneration of the BMF of 3,4 and 6-point (a singular point which is the intersection of 3 / 4 / 6 planes; see [6],[8]) were done. In this paper, we fill the gap and find the braid monodromy of the regeneration of a 5-point. This is of great importance to the understanding of the BMT (braid monodromy type) of surfaces [2]. This braid monodromy will be used to find the global braid monodromy factorization of different surfaces; in particular - the monodromy of the branch curve of the Hirzebruch surface F2,(2,2).

UR - http://www.scopus.com/inward/record.url?scp=57549116514&partnerID=8YFLogxK

U2 - 10.4310/pamq.2008.v4.n2.a5

DO - 10.4310/pamq.2008.v4.n2.a5

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AN - SCOPUS:57549116514

SN - 1558-8599

VL - 4

SP - 383

EP - 425

JO - Pure and Applied Mathematics Quarterly

JF - Pure and Applied Mathematics Quarterly

IS - 2 PART 1

ER -