275 problems

Let $f:({\mathbb C}^n,0)\rightarrow({\mathbb C},0)$ be a holomorphic function, with $n\ge 2$, and allow $f$ to have non-isolated singularities. The quantities $Q(f)$,…

Let $G$ satisfy the conditions of Theorem sf2, except that its discriminant need not be radial. For sufficiently small $\varepsilon>0$, consider the sphere $S^{m-1}_{\varepsilon}$…

Let $V_d^{\operatorname{irr}}(S_1,\dots,S_r)$ denote the family of reduced irreducible complex plane curves of degree $d$ with isolated singular points of prescribed topological ty…

Let $u,z,p_1,p_2,\ldots$ be indeterminates, let $p_\alpha=p_{\alpha_1}p_{\alpha_2}\cdots$, and define … For a partition $\alpha$ with $m$ parts, define…

Let $G\,|\,V$ be a polar representation, let $f:V\to Q$ be the quotient map, and set … An $A_f$ stratification is the stratification condition described in Section 2.2.1. The Af st…

Let $a_0, a_1,\dots,a_n\geq 2$, and let … be the $(2n-1)$-dimensional Brieskorn link. Let $\Gamma(a_0,a_1,\dots,a_n)$ be the graph with vertices $0,1,\dots,n$, joining $i$ and $j$…

Let $X$ be a projective algebraic variety of dimension $n$, let $W$ be a very ample linear system on $X$, and let $S_1,\dots,S_r$ be singularity types with Milnor numbers…

Fix a field $k$ and positive integers $p_0,\ldots,p_n>1$. For each $i$, let $W_{p_i}(X_i)\in\mathbb{C}[X_i]$ be a general polynomial of degree $p_i$, and set … Let…

Let $f$ be a singular function, let its bifurcation diagram be the relevant discriminant in the parameter space of a versal unfolding, and let the braid monodromy group be the imag…

Let $f$ and $g$ be singular functions such that $f$ is adjacent to $g$, so that a versal unfolding of $g$ is also a versal unfolding for $f$. Let $4mu$ and $tilde\mu$ be the corres…

Let $f$ be a singular function with Milnor number $4mu$, and let a Dynkin diagram of $f$ have vertex cardinality $4mu$. Write $t_1,\cdots,t_4mu$ for generators indexed by its vertic…

Let $f$ be a singular function and let a Dynkin diagram encode its algebraic monodromy. Consider the braid subgroup associated to such a Dynkin diagram, allowing conjugation in the…

Let $f$ be a singular function, with braid monodromy group acting by the Artin representation on its algebraic monodromy homomorphism. Stabilizer conjecture. The braid monodromy gr…

Let $(C,p_i)_{i=1}^\nu$ be a collection of locally irreducible local plane curve singularities satisfying … for some integer $d$. Let $c_l$ be the coefficients associated with the…

Let $f:({\mathbb C}^{n+1},0)\to({\mathbb C},0)$ be a germ of an analytic function, and let $Z_{top,0}(f,s)\in{\mathbb Q}(s)$ be its local topological zeta function. A pole $s_0$ of…

Assume $Y={\mathbb C}^{n+1}$ and that $f$ is weighted homogeneous. Let $C$ be the matrix of the monodromy operator $h_*$ on $H_n(X_\delta,{\mathbb C})$ with respect to a basis, let…

Let $W$ be a regular weight system and $f$ be a quasi-homogeneous polynomial attached to $W$. Assume $W$ has a dual regular weight system $W^*=(a^*,b^*,c^*;h)$ in the sense of K. S…

A Thom–Boardman class is a singularity class indexed by a sequence of nonnegative integers, and its Thom polynomial is the universal cohomology class representing the locus of maps…

Let $D$ be a free divisor in a complex manifold $X$. The logarithmic comparison conjecture. If the logarithmic comparison theorem holds for $D$, then $D$ is strongly Euler homogene…

Assume that the singular set of the limiting space has a stratification $B^{sing}=B^{sing}_{n-1}\cup B^{sing}_{\le n-2}$, where $B^{sing}_{n-1}$ consists of the $(n-1)$-dimensional…

Bernoulli-moment sign conjectures. For every $k\in{\mathbb N}$, both the weak form

Let $f$ be non-degenerate with respect to its Newton polyhedron, and let $\tau_{0}$ be a codimension-one simplex whose only lattice points in its intersection with the support of…

Let $f$ be a real analytic germ at $0\in\mathbb{R}^{n}$ with Newton polyhedron, and let $\tau_{0}$ be the face determining the relevant pole and coefficient $\mu(\varphi)$ of the a…

Let $(R,\mathfrak{m})$ be a $d$-dimensional F-finite F-pure non-$\mathbb{Q}$-Gorenstein normal local ring of characteristic $p>0$. Let $\mathrm{c}(\mathfrak{m})$ denote its F-pure…

Sector correspondence conjecture. The Neveu–Schwarz sectors are in one-to-one correspondence with the one-dimensional twisted sectors, while the Ramond sectors are in one-to-one co…