Free Divisors versus Stability and Coincidence Thresholds

Sticlaru, Gabriel

doi:10.9734/bjmcs/2014/8185

BJMCS

2014

DOI: 10.9734/bjmcs/2014/8185

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Free Divisors versus Stability and Coincidence Thresholds

Gabriel Sticlaru

Abstract: Abstract. We show that there is an unexpected relation between free divisors and stability and coincidence thresholds for projective hypersurfaces.

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2014

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The abelianization of the Johnson kernel

Dimca¹,

Hain²,

Papadima³

2014

J. Eur. Math. Soc.

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Abstract. We prove that the first complex homology of the Johnson subgroup of the Torelli group T g is a non-trivial, unipotent T g -module for all g ≥ 4 and give an explicit presentation of it as a Sym • H 1 (T g , C)-module when g ≥ 6. We do this by proving that, for a finitely generated group G satisfying an assumption close to formality, the triviality of the restricted characteristic variety implies that the first homology of its Johnson kernel K is a nilpotent module over the corresponding Laurent polynomial ring, isomorphic to the infinitesimal Alexander invariant of the associated graded Lie algebra of G. In this setup, we also obtain a precise nilpotence test.

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The abelianization of the Johnson kernel

Dimca¹,

Hain²,

Papadima³

2014

J. Eur. Math. Soc.

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Syzygies and logarithmic vector fields along plane curves

Dimca¹,

Sernesi²

2014

Journal De L’École Polytechnique — Mathématiques

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For a reduced curve C : f = 0 in the complex projective plane P 2 , we study the set of jumping lines for the rank two vector bundle T C on P 2 , whose sections are the logarithmic vector fields along C. We point out the relations of these jumping lines with the Lefschetz type properties of the Jacobian module of f and with the Bourbaki ideal of the module of Jacobian syzygies of f . In particular, when the vector bundle T C is unstable, a line is a jumping line if and only if it meets the 0-dimensional subscheme defined by this Bourbaki ideal, a result going back to Schwarzenberger. Other classical general results by Barth, Hartshorne and Hulek resurface in the study of this special class of rank two vector bundles.

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Free Divisors versus Stability and Coincidence Thresholds

Abstract: Abstract. We show that there is an unexpected relation between free divisors and stability and coincidence thresholds for projective hypersurfaces.

Cited by 2 publications

References 4 publications

The abelianization of the Johnson kernel

The abelianization of the Johnson kernel

Syzygies and logarithmic vector fields along plane curves

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