The theta divisor of SUC(2,2d)s is very ample if C is not hyperelliptic

Brivio, Sonia; Verra, Alessandro

doi:10.1215/s0012-7094-96-08222-8

Cited by 23 publications

(18 citation statements)

References 10 publications

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“…When d = 1, for example, L x = Kx 2 and 10.3 follows from [18] lemma 4.1. In the case d = 2, part 1 is proved in [5] proposition 4.9. Part 2 can also be shown-for g > 4 this will appear elsewhere, but in the case g = 4 we can give a simple ad hoc argument as follows.…”

Section: Appendix: Symmetric Products Of a Curvementioning

confidence: 89%

Heisenberg invariant quartics and  C (2) for a curve of genus four

Oxbury¹,

Pauly²

1999

Math. Proc. Camb. Phil. Soc.

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Section: Appendix: Symmetric Products Of a Curvementioning

confidence: 89%

Heisenberg invariant quartics and  C (2) for a curve of genus four

Oxbury¹,

Pauly²

1999

Math. Proc. Camb. Phil. Soc.

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“…Then, after the natural identification of these two linear systems, the next theorem follows. See [1,16]. It is now useful to summarize more informations from the literature on the embedding B ⊂ |2Θ| and the linear projection γ :…”

Section: The Theta Map γ : B → P 6 and The Coble Quarticmentioning

confidence: 99%

Edge and Fano on nets of quadrics

Verra

2018

European Journal of Mathematics

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In a number of papers by Edge, and in a related paper by Fano, several properties are discussed about the family of scrolls R ⊂ P 3 of degree 8 whose plane sections are projected bicanonical models of a genus 3 curve C. This beautiful classical subject is implicitely related to the moduli of semistable rank two vector bundles on C with bicanonical determinant. In this paper such a matter is reconstructed in modern terms from the modular point of view. In particular, the stratification of the family of scrolls R by Sing R is considered and the cases where R has multiplicity ≥ 3 along a curve are described.

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“…+ z 4 be an effective canonical divisor on C, D = (z i + C) be the corresponding divisor on S 2 C and ∆ be the diagonal in S 2 C. Then, 2K S 2 C = 2D − ∆. By [BV96,Lemma 4.7], we have the restriction sequence…”

Section: An Explicit Examplementioning

confidence: 99%

Genus three curves and 56 nodal sextic surfaces

Geemen

Zhao

2018

J. Algebraic Geom.

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Catanese and Tonoli showed that the maximal cardinality for an even set of nodes on a sextic surface is 56 and they constructed such nodal surfaces. In this paper we give an alternative, rather simple, construction for these surfaces starting from a non-hyperelliptic genus three curve. We illustrate our method by giving explicitly the equation of such a sextic surface starting from the Klein curve.

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The theta divisor of SUC(2,2d)s is very ample if C is not hyperelliptic

Cited by 23 publications

References 10 publications

Heisenberg invariant quartics and  C (2) for a curve of genus four

Heisenberg invariant quartics and  C (2) for a curve of genus four

Edge and Fano on nets of quadrics

Genus three curves and 56 nodal sextic surfaces

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