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http://cimat.repositorioinstitucional.mx/jspui/handle/1008/923| NON-EMPTINESS OF MODULI SPACES OF COHERENT SYSTEMS | |
| GLORIA LETICIA BRAMBILA PAZ | |
| Acceso Abierto | |
| Atribución-NoComercial-CompartirIgual | |
| Espacios de Moduli | |
| Let X be a general smooth projective algebraic curve of genus g ≥ 2 over C. We prove that the moduli space G(α : n, d, k) of α-stable coherent systems of type (n, d, k) over X is empty if k > n and the Brill–Noether number β := β(n, d, n+1) = β(1, d, n+1) = g − (n + 1)(n − d + g) < 0. Moreover, if 0 ≤ β < g or β = g, n |g and for some α > 0, G(α : n, d, k) = ∅ then G(α : n, d, k) = ∅ for all α > 0 and G(α : n, d, k) = G(α : n, d, k) for all α, α > 0 and the generic element is generated. In particular, G(α : n, d, n+1) = ∅ if 0 ≤ β ≤ g and α > 0. Moreover, if β > 0 G(α : n, d, n+1) is smooth and irreducible of dimension β(1, d,n+1).We define a dual span of a generically generated coherent system. We assume d < g + n1 ≤ g + n2 and prove that for all α > 0, G(α : n1, d,n1 + n2) = ∅ if and only if G(α : n2, d,n1 + n2) = ∅. For g = 2, we describe G(α : 2, d,k) for k > n. | |
| World Scientific | |
| 2008 | |
| Artículo | |
| Inglés | |
| Investigadores | |
| GEOMETRÍA ALGEBRAICA | |
| Versión publicada | |
| publishedVersion - Versión publicada | |
| Aparece en las colecciones: | Matemáticas |
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