Applications of braid group techniques to the decomposition of moduli spaces, new examples

A. Robb; M. Teicher

doi:10.1016/s0166-8641(96)00153-8

Applications of braid group techniques to the decomposition of moduli spaces, new examples

A. Robb
, M. Teicher

Department of Mathematics

Bar-Ilan University

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

Every smooth minimal complex algebraic surface of general type, X, may be mapped into a moduli space, M_c12(X),c₂(X), of minimal surfaces of general type, all of which have the same Chern numbers. Using the braid group and braid monodromy, we construct infinitely many new examples of pairs of minimal surfaces of general type which have the same Chern numbers and nonisomorphic fundamental groups. Unlike previous examples, our results include X for which |π₁(X)| is arbitrarily large. Moreover, the surfaces are of positive signature. This supports our goal of using the braid group and fundamental groups to decompose M_c12(X),c₂(X) into connected components.

Original language	English
Pages (from-to)	143-151
Number of pages	9
Journal	Topology and its Applications
Volume	78
Issue number	1-2
DOIs	https://doi.org/10.1016/s0166-8641(96)00153-8
State	Published - 1997

Keywords

Algebraic surfaces
Fundamental groups
Moduli spaces

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10.1016/s0166-8641(96)00153-8

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abstract = "Every smooth minimal complex algebraic surface of general type, X, may be mapped into a moduli space, Mc12(X),c2(X), of minimal surfaces of general type, all of which have the same Chern numbers. Using the braid group and braid monodromy, we construct infinitely many new examples of pairs of minimal surfaces of general type which have the same Chern numbers and nonisomorphic fundamental groups. Unlike previous examples, our results include X for which |π1(X)| is arbitrarily large. Moreover, the surfaces are of positive signature. This supports our goal of using the braid group and fundamental groups to decompose Mc12(X),c2(X) into connected components.",

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AB - Every smooth minimal complex algebraic surface of general type, X, may be mapped into a moduli space, Mc12(X),c2(X), of minimal surfaces of general type, all of which have the same Chern numbers. Using the braid group and braid monodromy, we construct infinitely many new examples of pairs of minimal surfaces of general type which have the same Chern numbers and nonisomorphic fundamental groups. Unlike previous examples, our results include X for which |π1(X)| is arbitrarily large. Moreover, the surfaces are of positive signature. This supports our goal of using the braid group and fundamental groups to decompose Mc12(X),c2(X) into connected components.

KW - Algebraic surfaces

KW - Fundamental groups

KW - Moduli spaces

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JO - Topology and its Applications

JF - Topology and its Applications

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Applications of braid group techniques to the decomposition of moduli spaces, new examples

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Keywords

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