7 problems

Let $QH=\mathbb{C}P^1\times\mathbb{C}P^1$ and let $\Sigma_2$ be the second Hirzebruch surface. For integers $a,b\geq 0$, let $\square_{a,b}$ and $\triangle_{a,b}$ denote the homolo…

Assume that $\mathbb{P}^2_k$ is obtained from $\mathbb{P}^2$ by blowing up $k$ generic real points and is equipped with its natural real structure. Let $D\subset \mathbb{P}^2_k$ be…

Asymptotic conjecture. For every fixed $r”\ge 0$,

Positivity and monotonicity conjecture. The invariants are positive for

Let $S_n$ be the blow-up of $\mathbb{P}^2$ at $n$ general real points, and let $\beta\in H_2(S_n,\mathbb{Z})$ be a curve class such that … Here $BPS_\beta^{S_n}(q)$ denotes the BPS…

Let $(\mathbb{R}P^1)^3$ be the product of three real projective lines with the standard real structure, and let $\mathfrak{s}_{(\mathbb{R}P^1)^3}$ be the $Spin_3$-structure over…

Let $d$ be a positive integer, and let $W_{\mathbb{R}P^3}(d,l)$ denote the Welschinger invariant of degree $d$ with the parameter $l$ specifying the real-point constraint. Equality…