Related papers: Smooth 3-dimensional canonical thresholds

We define a canonical quadratic pair on the Clifford algebra of an algebra with quadratic pair over a field. This allows us to extend to the characteristic 2 case the notion of trialitarian triples, from which we derive a characterization…

Let $Y$ be a generic link of a subvariety $X$ of a nonsingular variety $A$. We give a description of the Grauert-Riemenschneider canonical sheaf of $Y$ in terms of the multiplier ideal sheaves associated to $X$ and use it to study the…

The symbol $\mathcal{S}(X)$ denotes the hyperspace of finite unions of convergent sequences in a Hausdorff space $X$. This hyperspace is endowed with the Vietoris topology. First of all, we give a characterization of convergent sequence in…

We prove that $$ \cat X\le \frac{\cd(\pi_1(X))+\dim X}{2}$$ for every CW complex $X$ where $\cd(\pi_1(X))$ denotes the cohomological dimension of the fundamental group of $X$. We obtain this as a corollary of the inequality $$ \cat…

The discreteness problem, that is, the problem of determining whether or not a given finitely generated group G of orientation preserving isometries of hyperbolic three-space is discrete as a subgroup of the whole isometry group of…

In this note, we extend the theory of Chern-Cheeger-Simons to construct canonical invariants for a one-parameter family of flat connections on a smooth manifold. These invariants lie in degrees $(2p-2)$-cohomology with $\C/\Z$-cohomology,…

Motivated by DeVleming's work on moduli of surfaces in $\mathbb{P}^3$ and Chen-Hu-Jiang's work on moduli of threefolds with volume $2$ and geometric genus $4$, we study the deformation of pairs of $\mathbb{P}^3$ and hypersurfaces using the…

Smooth complex polarized varieties $(X,L)$ with a vector subspace $V \subseteq H^0(X,L)$ spanning $L$ are classified under the assumption that the locus ${\Cal D}(X,V)$ of singular elements of $|V|$ has codimension equal to $\dim(X)-i$,…

Tridiagonal canonical forms of square matrices under congruence or *congruence, pairs of symmetric or skew-symmetric matrices under congruence, and pairs of Hermitian matrices under *congruence are given over an algebraically closed field…

Let S be a minimal complex surface of general type with irregularity q>=2 and let C be an irreducible curve of geometric genus g contained in S. Assume that C is "Albanese defective", i.e., that the image of C via the Albanese map does not…

We determine the 6-dimensional solvmanifolds admitting an invariant complex structure with holomorphically trivial canonical bundle. Such complex structures are classified up to isomorphism, and the existence of strong K\"ahler with torsion…

Two measurable sets $S, \Lambda \subseteq \mathcal{R}^d$ form a Heisenberg uniqueness pair, if every bounded measure $\mu$ with support in S whose Fourier transform vanishes on {\Lambda} must be zero. We show that a quadratic hypersurface…

This thesis is devoted to the study of abelian automorphism groups of surfaces and $3$-folds of general type over complex number field $\Bbb C$. We obtain a linear bound in $K^3$ for abelian automorphism groups of $3$-folds of general type…

Let $P_{\text{MAX}}(d,s)$ denote the maximum arithmetic genus of a locally Cohen-Macaulay curve of degree $d$ in $\mathbb{P}^3$ that is not contained in a surface of degree $<s$. A bound $P(d, s)$ for $P_{\text{MAX}}(d,s)$ has been proven…

Let $X \subset \mathbb{P}^{n+1}$ be a smooth Fano hypersurface of dimension $n$ and degree $d$. The derived category of coherent sheaves on $X$ contains an interesting subcategory called the Kuznetsov component $\mathcal{A}_X$. We show that…

By developing a suitable version of the circle method, we show that the space of degree $e$ rational curves on a smooth hypersurface of degree $d$ has only canonical singularities provided its dimension is sufficiently large with respect to…

Categorical resolutions of singularities are a replacement of resolution of singularities within the realm of triangulated categories. They allow the study of the derived category of a singular variety $X$ via a triangulated category that…

A finite subgroup of the conformal group SL(2,C) can be related to invariant polynomials on a hypersurface in C^3. The latter then carries a simple singularity, which resolves by a finite iteration of basic cycles of deprojections. The…

The splice quotients are an interesting class of normal surface singularities with rational homology sphere links, defined by W. Neumann and J. Wahl. If Gamma is a tree of rational curves that satisfies certain combinatorial conditions,…

For a characteristic $p > 0$ variety $X$ with controlled $F$-singularities, we state conditions which imply that a divisorial sheaf is Cohen-Macaulay or at least has depth $\geq 3$ at certain points. This mirrors results of Koll\'ar for…