3 1 M ay 2 00 2 Green ’ s generic syzygy conjecture for curves of even genus lying on a K 3 surface Claire
نویسنده
چکیده
for X a variety and L a line bundle on X. Denoting by Kp,q(X,L) the cohomology at the middle of the sequence above, one sees immediately that the surjectivity of the map μ0 is equivalent to K0,2(C,KC) = 0, and that if this is the case, the ideal I is generated by quadrics if and only if K1,2(C,KC) = 0. On the other hand, C being non hyperelliptic is equivalent to the fact that the Clifford index Cliff C is strictly positive, where
منابع مشابه
m at h . A G ] 1 6 M ay 2 00 3 Green ’ s canonical syzygy conjecture for generic curves of odd genus Claire Voisin
The direction ⇒ is proved by Green and Lazarsfeld in the appendix to [3]. The case p = g − 2 of the conjecture is equivalent to Noether’s theorem, and the case p = g − 3 to Petri’s theorem (see [5]). The case p = g − 4 has been proved in any genus by Schreyer [9] and by the author [12] for g > 10. More recently, the conjecture has been studied in [10], [11], for generic curves of fixed gonality...
متن کاملGreen ’ s canonical syzygy conjecture for generic curves of odd genus Claire Voisin
The direction ⇒ is proved by Green and Lazarsfeld in the appendix to [4]. The case p = g − 2 of the conjecture is equivalent to Noether’s theorem, and the case p = g − 3 to Petri’s theorem (see [6]). The case p = g − 4 has been proved in any genus by Schreyer [10] and by the author [13] for g > 10. More recently, the conjecture has been studied in [11], [12], for generic curves of fixed gonalit...
متن کاملGreen’s canonical syzygy conjecture for generic curves of odd genus
The direction ⇒ is proved by Green and Lazarsfeld in the appendix to [3]. The case p = g−2 of the conjecture is equivalent to Noether’s theorem, and the case p = g−3 to Petri’s theorem (see [5]). The case p = g − 4 has been proved in any genus by Schreyer [9] and by the author [13] for g > 10. More recently, the conjecture has been studied in [11], [12], for generic curves of fixed gonality. Te...
متن کاملGreen’s generic syzygy conjecture for curves of even genus lying on a K3 surface
for X a variety and L a line bundle on X. Denoting by Kp,q(X,L) the cohomology at the middle of the sequence above, one sees immediately that the surjectivity of the map μ0 is equivalent to K0,2(C, KC) = 0, and that if this is the case, the ideal I is generated by quadrics if and only if K1,2(C, KC) = 0. On the other hand, C being non hyperelliptic is equivalent to the fact that the Clifford in...
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We discuss the role of K3 surfaces in the context of Mercat’s conjecture in higher rank Brill–Noether theory. Using liftings of Koszul classes, we show that Mercat’s conjecture in rank 2 fails for any number of sections and for any gonality stratum along a Noether– Lefschetz divisor inside the locus of curves lying on K3 surfaces. Then we show that Mercat’s conjecture in rank 3 fails even for c...
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