3 problems

Let $X=\mathbb{C}^4$, let $E=\bigoplus_{i=1}^{N}\mathcal{O}_X\langle y_i\rangle$ and $V=\bigoplus_{i=1}^{r}\mathcal{O}_X\langle v_i\rangle$, and let $\alpha\in K_{\mathsf{T}}(X)$.…

Let $A_0(q),A_1(q),B_0(q),B_1(q)$ be the series introduced from the degree-zero reduced Segre and Verlinde series, with $N=1$. Degree-zero coefficient formulas. For…

Let $r,N>0$, let $S=\mathbb{C}^2$, and set $E=\bigoplus_{i=1}^N\mathcal{O}_S\langle y_i\rangle$ and $V=\bigoplus_{i=1}^r\mathcal{O}_S\langle v_i\rangle$. Strong Segre symmetry. The…