18 problems

Spanning conjecture. If $k eleq r eleq 2k-n-2$, then $(Rn/(E+(Q-1)))r$ is spanned by the expressions in the generating family for which $i1<(n-1)+(r-k)$; if $k-n<r<k$, the expressi…

Orlik–Randell conjecture. For the fiber $X_1=\operatorname{Var}(Q-1)$, there is a finite-dimensional homogeneous vector space $U\subset R_n$ such that

Bobadilla's conjecture. Under these assumptions, $\Sigma f$ is smooth at $\mathbf 0$.

Torsion conjecture for Milnor fiber boundaries. (1) If

Let two hypersurface singularities be ambient-homeomorphic if their ambient spaces and singularities are related by an ambient homeomorphism, and let $F_f$ denote the Milnor fiber…

Let $f$ be a complex analytic function in $d$ variables vanishing at the origin $O$. Let $F_{f,O}$ be its topological Milnor fiber, let $\mathscr S_{f,O}$ be the motivic Milnor fib…

Milnor fiber conjecture. The Milnor fiber of $(X,o)$ is obtained by a four-dimensional splicing operation from the Milnor fibers associated to $\Gamma_a$ and $\Gamma_b$.

Casson invariant conjecture. The Casson invariant of $\partial(X,o)$ is equal to one-eighth of the signature of the Milnor fiber of $(X,o)$.

Splice-diagram decomposition conjecture. The Milnor fiber $F$ is homeomorphic to the result $\overline F$ of pasting

Casson invariant conjecture. The Casson invariant of $a3$ equals one-eighth the signature of the Milnor fiber.

Let $M$ be a surface Milnor fiber of an $ADE$-type singularity, with its standard zero sections and standard Lagrangian spheres. ADE Lagrangian-sphere conjecture. Every Lagrangian…

Let ${\mathcal A}$ be a real arrangement, let $F$ be its Milnor fiber, and let monodromy mean the action induced on the homology of $F$. A nontrivial monodromy has prime-power orde…

Let ${\mathcal A}$ be a real affine line arrangement and let $\overline{{\mathcal A}}$ be its projective arrangement. A sharp pair of lines is a pair of projective lines satisfying…

Let ${\mathcal A}$ be a real affine line arrangement, and let $\Gamma({\mathcal A})$ be the graph whose vertices are the lines $H\in{\mathcal A}$, with an edge $(H,H')$ exactly whe…

Let $\mathcal{U}$ be an open neighborhood of the origin in $\mathbb{C}^{n+1}$, let $f:(\mathcal{U},\mathbf{0})\to(\mathbb{C},0)$ be a complex analytic function with…

Let $f$ be a holomorphic function germ with critical locus $\boldsymbol{\Sigma} f$, let $F_{f,\mathbf 0}$ denote its Milnor fiber at the origin, and let $\stackrel{\circ}{\mu}_C$ b…

Let $f$ be a holomorphic function germ with critical locus $\boldsymbol{\Sigma} f$, let $C$ be its irreducible component, and let $F_{f,\mathbf p}$ denote the Milnor fiber of $f$ a…

Let $c\mathcal{A}$ be the cone over a real line arrangement $\mathcal{A}$, and suppose that $c\mathcal{A}$ is a simplicial arrangement. Let $F_{\mathcal{A}}$ denote the Milnor fibe…