7 problems

Let $f\in\mathbb{C}[[x,y,z]]$ be an isolated hypersurface singularity. Let $\mu$ be its Milnor number and $p_g$ its geometric genus. Durfee's conjecture. … with equality only when…

Let $(X,0)$ be a Gorenstein normal surface singularity with link $M$, and suppose that $M$ is a rational homology sphere. A property is topological if it can be determined from the…

Let $n=2\ell$, assume that $\operatorname{char}(F)$ is zero or sufficiently positive, and let $\mathcal{C}_m$ be the $m$-th inflectionary curve from $y^n=x^5+x^3+sx$. D4 genus conj…

Let $n=2\ell$, let $F$ have characteristic zero or sufficiently positive characteristic, and let $\mathcal{C}^{\ell}_m\subset\mathbb{P}(1,2,1)$ be the inflectionary curve derived f…

Geometric genus conjecture. There is a smooth hypersurface $D\in|\mathcal{O}_X(L)|$ carrying an $s$-dimensional subvariety $S\subset D$ of geometric genus $g$.

Let $(X,0)$ be a Gorenstein normal surface singularity, let $M$ be its link, and let $p_g$ denote the geometric genus of $(X,0)$. Assume that $M$ has trivial first homology with ra…

Corrected Durfee inequalities. One has the following bounds: