The Generic Green-lazarsfeld Secant Conjecture
نویسندگان
چکیده
Using lattice theory on specialK3 surfaces, calculations on moduli stacks of pointed curves and Voisin’s proof of Green’s Conjecture on syzygies of canonical curves, we prove the Prym-Green Conjecture on the naturality of the resolution of a general Prym-canonical curve of odd genus, as well as (many cases of) the Green-Lazarsfeld Secant Conjecture on syzygies of non-special line bundles on general curves.
منابع مشابه
The Extremal Secant Conjecture for Curves of Arbitrary Gonality
We prove the Green–Lazarsfeld Secant Conjecture [GL1, Conjecture (3.4)] for extremal line bundles on curves of arbitrary gonality, subject to explicit genericity assumptions.
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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...
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These notes discuss recent advances on syzygies on algebraic curves, especially concerning the Green, the Prym-Green and the Green-Lazarsfeld Secant Conjectures. The methods used are largely geometric and variational, with a special emphasis on examples and explicit calculations. The notes are based on series of lectures given in Daejeon (March 2013), Rome (November-December 2015) and Guanajuat...
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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 کاملm 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...
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