Related papers: On singularities of determinantal hypersurfaces

For separable metrizable spaces $X,Y$ and a metrizable topological group $Z$ by $S(X\times Y,Z)$ we denote the space of all separately continuous functions $f:X\times Y\to Z$ endowed with the topology of layer-wise uniform convergence,…

Let X and Y be finite nilpotent CW complexes with dimension of X less than the connectivity of Y. Generalizing results of Vigu\'e-Poirrier and Yamaguchi, we prove that the mapping space Map(X,Y) is rationally formal if and only if Y has the…

We give a proof to the following theorem, which is well-known among experts: A connected subcomplex $W$ of a finite dimensional CAT(0) cubed complex $X$ is convex if and only if Lk$(v, W)$ is a full subcomplex of Lk$(v, X)$ for every vertex…

Let $\mathfrak{P}_r$ be a representation system of the non-isomorphic finite posets, and let ${\cal H}(P,Q)$ be the set of order homomorphisms from $P$ to $Q$. For finite posets $R$ and $S$, we write $R \sqsubseteq_G S$ iff, for every $P…

Let $X$ be an algebraic variety with Gorenstein singularities. We define the notion of a wonderful resolution of singularities of $X$ by analogy with the theory of wonderful compactifications of semi-simple linear algebraic groups. We prove…

This paper is concerned with singular projective rationally connected threefolds $X$ which carry non-zero pluri-forms, \textit{i.e.} $H^0(X,(\Omega_X^1)^{[\otimes m]}) \neq \{0\}$ for some $m > 0$, where $(\Omega_X^1)^{[\otimes m]}$ is the…

Let $R$ be a hypersurface in an equicharacteristic or unramified regular local ring. For a pair of modules $(M,N)$ over $R$ we study applications of rigidity of $\Tor^R(M,N)$, based on ideas by Huneke, Wiegand and Jorgensen. We then focus…

We consider suspension hypersurface singularities of type g=f(x,y)+z^n, where f is an irreducible plane curve singularity. For such germs, we prove that the link of g determines completely the Newton pairs of f and the integer n except for…

Let $X$ and $Y$ be proper birational varieties, say with only rational double points over a perfect field $k$ of positive characteristic. If $X$ lifts to $W_n(k)$, is it true that $Y$ has the same lifting property? This is true for smooth…

In this paper, we study the singularities of a general hyperplane section $H$ of a three-dimensional quasi-projective variety $X$ over an algebraically closed field of characteristic $p>0$. We prove that if $X$ has only canonical…

In this paper we study rational surface singularities R with star shaped dual graphs, and under very mild assumptions on the self-intersection numbers we give an explicit description of all their special Cohen-Macaulay modules. We do this…

Let $\mathbb{W}$ be an irreducible subvariety a Hilbert scheme $Hilb_{p_W} (t) (\mathbb{P}^n )$. We show that under mild hypothesis there are polynomial formulas for the degrees of the loci of hypersurfaces in $\mathbb{P}^n$ with singular…

We apply the local removable singularity theorem for minimal laminations and the local picture theorem on the scale of topology to obtain two descriptive results for certain possibly singular minimal laminations of $\mathbb{R}^3$. These two…

We discuss a particular class of rational Gorenstein singularities, which we call symplectic. A normal variety V has symplectic singularities if its smooth part carries a closed symplectic 2-form whose pull-back in any resolution X --> V…

Let $ G = \mathbb{Z}/r\mathbb{Z}$ be the cyclic group of order $r$, and let $\varpi = e^{2\pi i / r}$ denote a primitive $r$ th root of unity. Consider the action of $G$ on $\mathbb{C}^n$ via the embedding $$ \varphi : G \hookrightarrow…

In this paper we classify all singular irreducible symplectic surfaces, i.e., compact, connected complex surfaces with canonical singularities that have a holomorphic symplectic form $\sigma$ on the smooth locus, and for which every finite…

A classical result of singularity theory states that the spectrum of an isolated hypersurface singularity is symmetric with respect to $n/2$, where $n$ is the dimension of the enclosing space. We prove a similar result for the…

In this paper we give a necessary combinatorial condition for a negative--definite plumbing tree to be suitable for rational blow--down, or to be the graph of a complex surface singularity which admits a rational homology disk smoothing.…

Let (M,p) and (M',p') be the germs of real-analytic 1-infinite type hypersurfaces in \C^2. We prove that any formal equivalence sending (M,p) into (M',p') is formally parametrized (and hence uniquely determined by) its jet at p of a…

A lattice is called well-rounded if its minimal vectors span the corresponding Euclidean space. In this paper we completely describe well-rounded full-rank sublattices of ${\mathbb Z}^2$, as well as their determinant and minima sets. We…