منابع مشابه
Brill-noether Theory
Let us be more precise. Of course, it is tautological that any projective curve can be embedded into some projective space. However, once we begin making demands on the embedding, we start to get some interesting answers. For instance, can we make sure target projective space “small”? It is easy to show that not every curve can be embedded in P2. Conversely, every smooth projective curve can be...
متن کاملBrill-noether Theory, Ii
This article follows the paper of Griffiths and Harris, "On the variety of special linear systems on a general algebraic curve." 1. WARMUP ON DEGENERATIONS The classic first problem in Schubert calculus is: how many lines intersect four general lines in P 3 ? First, what does this numerology come from? The space of lines in P 3 is G(1, 3) which has dimension 2 × 2 = 4. The locus of lines inters...
متن کاملAlgebraic and combinatorial Brill-Noether theory
The interplay between algebro-geometric and combinatorial Brill-Noether theory is studied. The Brill-Noether locus W r d (Γ) of a genus-g (non-metric) graph Γ is shown to be non-empty if the BrillNoether number ρd(g) is non-negative, as a consequence of the analogous fact for smooth projective curves. Similarly, the existence of a graph Γ for which W r d (Γ) is empty implies the emptiness of W ...
متن کاملBrill–Noether with ramification at unassigned points
We discuss, how via limit linear series and standard facts about divisors on moduli spaces of pointed curves, one can establish a non-existence Brill–Noether results for linear series with prescribed ramification at unassigned points. © 2013 Elsevier B.V. All rights reserved. In the course of developing their theory of limit linear series, among many other applications, Eisenbud and Harris [2,3...
متن کاملVector Bundles and Brill–Noether Theory
After a quick review of the Picard variety and Brill–Noether theory, we generalize them to holomorphic rank-two vector bundles of canonical determinant over a compact Riemann surface. We propose several problems of Brill–Noether type for such bundles and announce some of our results concerning the Brill–Noether loci and Fano threefolds. For example, the locus of rank-two bundles of canonical de...
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ژورنال
عنوان ژورنال: Journal of Differential Geometry
سال: 1986
ISSN: 0022-040X
DOI: 10.4310/jdg/1214440116