Mathematics – Algebraic Geometry
Scientific paper
2002-02-14
"Scrollar Syzygies of general canonical curves with genus at most 8", Trans. Amer. Math. Soc. 359 (2007), 465-488.
Mathematics
Algebraic Geometry
44 pages; 1 figure; AMSlatex. Author-supplied PDF file with graphics is available at http://btm8x5.mat.uni-bayreuth.de/~bothme
Scientific paper
10.1090/S0002-9947-06-04353-4
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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