6 problems

Modified positivity conjecture for complete intersections. For every integer $j$ with $0\leq j\leq n/2$,

Let $n$ be a positive integer, let $\mathbb{P}^n$ be complex projective space, and let $L^{2j}(\mathbb{P}^n)\in H^{4j}(\mathbb{P}^n,\mathbb{Q})$ denote its degree-$4j$ cohomology…

Constant and intersection-complex $L$-class conjecture. If $X$ is a ${\mathbb Q}$-homology manifold, then

Let $X$ be a compact complex algebraic variety that is a rational homology manifold. Denote by $T_{1*}(X)$ its Hodge-L-class and by $L_*(X)$ its topological Goresky–MacPherson L-cl…

Let $\Omega(-)$ denote the domain of Cappell--Shaneson's L-class transformations, and consider a natural transformation … without the normalization condition. Let ${L_*^{CS}}_i$ de…

Let $X$ be a rational homology manifold. Let ${T_1}_*(X)$ denote the specialization at $y=1$ of the motivic Hirzebruch class, and let $L_*^{GM}(X)$ denote the Goresky--MacPherson…