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Geometric Syzygies of Mukai Varieties and General Canonical Curves with Genus at most 8

Hans-Christian v. Bothmer
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Abstract

We describe the spaces of minimal rank last syzygies for the Mukai Varieties of sectional genus 6,7 and 8. Based on this we show: 1. The first geometric syzygies of a general canonical curve of genus 6 form a non degenerate configuration of 5 lines in P^4. 2. The first geometric syzygies of a general canonical curve of genus 7 form a non degenerate, linearly normal, ruled surface of degree 84 on a spinor variety S in P^15. 3. The second geometric syzygies of a general canonical curve of genus 8 form a non degenerate configuration of 14 conics on a 2-uple embedded P^5 in P^20. This proves a natural generalization of Green's conjecture [1984], namely that the geometric syzygies should span the space of all syzygies, in these cases. We have generalized results 1 and 3 to general curves of even genus in math.AG/0108078. Result 2 is the main new result of this paper.

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Hans-Christian v. Bothmer. 2002-02-14. Geometric Syzygies of Mukai Varieties and General Canonical Curves with Genus at most 8. https://doi.org/10.1090/s0002-9947-06-04353-4

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