next | previous | forward | backward | up | top | index | toc | Macaulay2 website
ConformalBlocks :: conformalBlockDegreeM04bar

conformalBlockDegreeM04bar -- computes the degree of a conformal block bundle on $\bar{M}_{0,4}$



This function implements the formula given in [Fakh] Corollary 3.5 for computing the degree of a conformal block vector bundle $V$ on $\bar{M}_{0,4}$.

The first line of the example below shows that the conformal block bundle $V(sl_3,1,(\omega_1,\omega_1,\omega_2,\omega_2))$ has degree 1 on $\bar{M}_{0,4} \cong \mathbb{P}^1$. The second line shows that this vector bundle is a line bundle. Hence, $V(sl_3,1,(\omega_1,\omega_1,\omega_2,\omega_2))$ is isomorphic to $\mathcal{O}(1)$.

i1 : sl_3 = simpleLieAlgebra("A",2);
i2 : V=conformalBlockVectorBundle(sl_3,1,{{1,0},{1,0},{0,1},{0,1}},0);
i3 : conformalBlockDegreeM04bar(V)

o3 = 1
i4 : conformalBlockRank(V)

o4 = 1

Ways to use conformalBlockDegreeM04bar :

For the programmer

The object conformalBlockDegreeM04bar is a method function.