3 problems

Let $Y=\mathbb{C}^d$, let $N>1$, set $E=\bigoplus_{i=1}^{N}\mathcal{O}_Y\langle y_i\rangle$, and, for $r=0,1,\ldots,N-2$, set $V=\bigoplus_{i=1}^{r}\mathcal{O}_Y\langle v_i\rangle$…

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…