Subbundles of maximal degree

Maximal Subbundles and Gromov-witten Invariants

Let C be a nonsingular irreducible projective curve of genus g ≥ 2 defined over the complex numbers. Suppose that 1 ≤ n ′ ≤ n − 1 and n ′ d − nd ′ = n ′ (n − n ′)(g − 1). It is known that, for the general vector bundle E of rank n and degree d, the maximal degree of a subbundle of E of rank n ′ is d ′ and that there are finitely many such subbundles. We obtain a formula for the number of these ...

L 10 Maximal Subbundles and Gromov - Witten Invariants

Let C be a nonsingular irreducible projective curve of genus g ≥ 2 defined over the complex numbers. Suppose that 1 ≤ n ′ ≤ n − 1 and n ′ d − nd ′ = n ′ (n − n ′)(g − 1). It is known that, for the general vector bundle E of rank n and degree d, the maximal degree of a subbundle of E of rank n ′ is d ′ and that there are finitely many such subbundles. We obtain a formula for the number of these ...

On the Maximal Degree of the K-Step Obrechkoff’s Method

M ay 2 00 0 Families of maximal subbundles of stable vector bundles on curves

Let X be a smooth projective curve of genus g ≥ 2 and let E be a vector bundle on X. Let Mk(E) be the scheme of all rank k subbundles of E with maximal degree. For every integers r, k and x with 0 < k < r and either 2k ≤ r and 0 ≤ x ≤ (k−1)(r−2k+1) or 2k > r and 0 ≤ x ≤ (r − k − 1)(2k − r + 1), we construct a rank r stable vector bundles E such that Mk(E) has an irreducible component of dimensi...

Isotropic subbundles of TM ⊕ T ∗

We define integrable, big-isotropic structures on a manifold M as subbundles E ⊆ T M ⊕ T * M that are isotropic with respect to the natural, neutral metric (pairing) g of T M ⊕ T * M and are closed by Courant brackets (this also implies that [E, E ⊥g ] ⊆ E ⊥g). We give the interpretation of such a structure by objects of M , we discuss the local geometry of the structure and we give a reduction...