Coherent systems on curves of compact type

Brivio, Sonia; Favale, Filippo F.

doi:10.1016/j.geomphys.2020.103850

Cited by 8 publications

(8 citation statements)

References 13 publications

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“…Finally, we recall the notion of coherent system on a polarized nodal curve (C, w) (see [BF20] for details). We refer to [BGPMN03] for treatment of the smooth case.…”

Section: Notations and Preliminary Resultsmentioning

confidence: 99%

Higher-rank Brill-Noether loci on nodal reducible curves

Brivio¹,

Favale²

2022

Preprint

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In this paper, we deal with Brill-Noether theory for higher-rank sheaves on a polarized nodal reducible curve (C, w) following the ideas of [BPGN97]. We study the Brill-Noether loci of w-stable depth one sheaves on C having rank r on all irreducible components and having small slope. In analogy with what happens in the smooth case, we prove that these loci are closely related to BGN extensions. Moreover, we produce irreducible components of the expected dimension for these Brill-Noether loci.

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“…Finally, we recall the notion of coherent system on a polarized nodal curve (C, w) (see [BF20] for details). We refer to [BGPMN03] for treatment of the smooth case.…”

Section: Notations and Preliminary Resultsmentioning

confidence: 99%

Higher-rank Brill-Noether loci on nodal reducible curves

Brivio¹,

Favale²

2022

Preprint

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“…For a reducible nodal curve, the components of the moduli space M(n, d) were determined in [Tei91b,Tei95] together with a useful criterion for the existence of stable bundles. For recent work on coherent systems on reducible nodal curves, see [BrF20b,BrF21]. The failure of Butler's conjecture on a reducible nodal curve with 2 components and one node is discussed in [BrF20a].…”

Section: Final Remarksmentioning

confidence: 99%

Higher rank Brill-Noether theory and coherent systems: Open questions

Newstead¹

2021

Preprint

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“…The case of singular, but integral curves, mainly nodal curves, is discussed in work of U. N. Bhosle [Bh2,Bh3] and references therein. The case of reducible curves appeared in [Bh1,BF1,BF2] and we will discuss it in subsection 4.3. Further classical results of Brill-Noether theory appear in [LN2,LN3,LN4,LNP,LNS].…”

Section: Brill-noether Theorymentioning

confidence: 99%

“…Thus, the arithmetic genera satisfy p a (X) = p a (X 1 ) + p a (X 2 ) and the integers (p a (X 1 ), p a (X 2 )) are the only numerical invariants of X. If p a (X i ) ≥ 3 for some i, even the Brill-Noether theory of line bundles on X, may depend on the isomorphic classes of X. S. Brivio and F. Favale [BF2] proved that for this reducible curve Butler's conjecture fails quite often, in non-pathological cases. Question 14.…”

Section: Brill-noether Theorymentioning

confidence: 99%