6 problems

Let $X$ be a smooth projective threefold with a smooth divisor $D$, let $\beta\in H_2(X,\mathbb{Z})$, and let $\eta$ be a relative partition. Write…

Let $f:X\to Y$ be a surjective morphism between smooth projective varieties with $\dim Y=n$, let $\mathcal L$ be any ample invertible sheaf on $Y$, and let $k$ be a positive intege…

Let $X$ be a smooth projective $3$-fold over $\mathbb{C}$ and let $S\subset X$ be a nonsingular divisor. Let $I_0(X/S,n)$ be the moduli space of relative ideal sheaves, define … an…

Let $X/D$ be a relative $3$-fold, let $\beta$ be a curve class, let $\mu$ be a relative boundary condition, and let $\gamma_i\in H^*(X)$. The barred relative descendent insertion i…

Let $X/D$ be a nonsingular projective relative $3$-fold. For a partition $\mu$ of $\int_\beta[D]$, write $|\mu|=\int_\beta D$, let $\ell(\mu)$ be its length, and set…

Let $f:X\to S$ be a surjective proper Kähler morphism with connected fibers between connected complex manifolds, let $S^{\circ}$ be the complement of the discriminant locus, and le…