The Maximal Rank Conjecture and Rank Two Brill-Noether Theory
نویسندگان
چکیده
منابع مشابه
The Maximal Rank Conjecture and Rank Two Brill-Noether Theory
We describe applications of Koszul cohomology to the BrillNoether theory of rank 2 vector bundles. Among other things, we show that in every genus g > 10, there exist curves invalidating Mercat’s Conjecture for rank 2 bundles. On the other hand, we prove that Mercat’s Conjecture holds for general curves of bounded genus, and its failure locus is a Koszul divisor in the moduli space of curves. W...
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Continuing our previous study of modified expected dimensions for rank-2 Brill-Noether loci with prescribed special determinants, we introduce a general framework which applies a priori for arbitrary rank, and use it to prove modified expected dimension bounds in several new cases, applying both to rank 2 and to higher rank. The main tool is the introduction of generalized alternating Grassmann...
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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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Let C be a general curve of genus g, embedded in Pr via a general linear series of degree d. In this paper, we prove the Maximal Rank Conjecture, which determines the Hilbert function of C ⊂ Pr.
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In the 1990’s, Bertram, Feinberg and Mukai examined Brill-Noether loci for vector bundles of rank 2 with fixed canonical determinant, noting that the dimension was always bigger in this case than the naive expectation. We generalize their results to treat a much broader range of fixed-determinant Brill-Noether loci. The main technique is a careful study of symplectic Grassmannians and related c...
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ژورنال
عنوان ژورنال: Pure and Applied Mathematics Quarterly
سال: 2011
ISSN: 1558-8599,1558-8602
DOI: 10.4310/pamq.2011.v7.n4.a9