Linear stability and stability of Lazarsfeld-Mukai bundles

Castorena, Abel; Torres-López, H.

doi:10.48550/arxiv.1705.06829

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Syzygy Bundles and Theta Divisors1

Cohomologically Semistable1

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2019

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Cited by 1 publication

(2 citation statements)

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“…Let L ∈ P ic d (C) be a globally generated line bundle over a general curve C of genus g with h 0 (L) = r+1. In ( [3], Corollary 4.3), the authors proved that the syzygy bundle M L is semistable (not stable) if and only if all the following three conditions hold:…”

Section: Syzygy Bundles and Theta Divisorsmentioning

confidence: 99%

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New examples of theta divisors for some syzygy bundles

Castorena

Torres-López

2019

European Journal of Mathematics

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Let C be a smooth complex irreducible projective curve of genus g with general moduli, and let (L, H 0 (L)) be a generated complete linear series of type (d, r + 1) over C. The syzygy bundle, denoted by ML, is the kernel of the evaluation map H 0 (L) ⊗ OC → L. In this work we have a double purpose. The first one is to give new examples of stable syzygy bundles admitting theta divisor over general curves. We prove that if ML is strictly semistable then ML admits reducible theta divisor. The second purpose is to study the cohomological semistability of ML, and in this direction we show that when L induces a birational map, the syzygy bundle ML is cohomologically semistable, and we obtain precise conditions for the cohomological semistability of ML where such conditions agree with the semistability conditions for ML.

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Section: Syzygy Bundles and Theta Divisorsmentioning

confidence: 99%

“…In ( [3], Corollary 4.3) the authors prove that the syzygy bundle M L is semistable (not stable) if and only if all the following three conditions hold:…”

Section: Cohomologically Semistablementioning

confidence: 99%