WebAug 1, 2024 · For example, instead of taking $\kappa$ to be the identity, we could embed $\mathbf P^2$ in $\mathbf P^5$ by the Veronese embedding, and that would multiply the … WebarXiv:math/0403033v1 [math.AG] 2 Mar 2004 VANISHING OF THE TOP CHERN CLASSES OF THE MODULI OF VECTOR BUNDLES YOUNG-HOON KIEM AND JUN LI AND JUN LI 0. Introduction Let Ybe a smooth
Math 396. Determinant bundles Preliminaries - Stanford …
WebMar 18, 2015 · The determinant of S y m k ( E) is ( det E) m, with m = ( r + k − 1 r); this follows from the analogous equality of G L ( V) -modules det ( S y m k ( V)) = ( det V) m … WebNow for V, V ′ vector bundles on any curve C its true that deg V ⊗ V ′ = deg V ⋅ r k ( V ′) + deg V ′ ⋅ r k ( V). So in the case of an elliptic curve the set I n d ( 0, r) is a torsor for P i c 0 ( C). Additionally, there is a unique isomorphism class V r ∈ I n d ( 0, r) characterized by the fact that h 0 ( V r) ≠ 0 (in fact h ... the rain is coming down in sheets
Holomorphic vector bundle - Wikipedia
WebDec 5, 2011 · The moduli space of stable vector bundles over of rank and degree was first given by Mumford and Seshadri .Later, Gieseker gave a different construction which … WebAdd a comment. 1. [Really a comment sed hac marginis ... .] a-fortiori's answer disposes of the question completely, but it is possible to go a little further: if V is a degree 0 sub-bundle of a free bundle on a curve, then V is free (and is a direct summand). Proof: Write W = V ∨, the dual bundle. Web$\begingroup$ In chapter 17 of Abelian Varieties, Theta Functions and the Fourier Transform, Polishchuk goes through a similar construction to the one you outline above in a characteristic free way. It uses the Fourier-Mukai transform of a line bundles on degree g-1 on your curve. I wouldn't say its any simpler than the construction you outlined but it … signs a relationship is over for men