4 problems

Let $V$ be a surface with geometric genus $p_g(V)>0$, and let $P^+_V(m)$ and $P^-_V(m)$ be the two Poincaré invariants associated with a class $m\to H^2(V,\mathbb{Z})$. Equality of…

Let $V$ be a smooth projective surface. Denote by $P^\bullet_V$ its Poincaré invariants and by $SW^\bullet_V$ its full Seiberg–Witten invariants, with the canonical orientation dat…

Poincaré–Seiberg–Witten correspondence conjecture. If $p_g(V)=0$, then

Let $X$ be an algebraic surface and let $\gamma\in H_2(X,\mathbb{Z})$. The Hilbert scheme $Hilb_X^\gamma$ parametrizes divisors $D$ on $X$ with homology class $\gamma$ and carries…