相关论文: Pre-foliations of co-degree one on $\mathbb{P}^{2}…

Fix a noetherian scheme S. For any flat map f: X->Y of separated essentially-finite-type perfect S-schemes we define a canonical derived-category map c(f):\H(X)->f^!\H(Y), the fundamental class of f, where \H(Z) is the (pre-)Hochschild…

We introduce a new equivalence relation, denoted by $A.Q.E.D.$ (= Algebraic-Quasi-\'Etale- Deformation) for complete algebraic varieties with canonical singularities: it is generated by birational equivalence, by flat algebraic…

BF theory is a topological field theory that appears in different parts of theoretical physics and one of its important uses is in lower dimensional holography settings. While it can be defined as a dimensional reduction of 3D CS theory, it…

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…

In this paper, which is a natural continuation of our previous paper math.DG/0504557, we describe some special Lagrangians of cohomogeneity one in the resolved conifold. Our main result gives a foliation of the resolved conifold by…

Let $p$ be a prime. We resolve a question posed by Min\'a\v{c}-Rogelstad-T\^an. We relate the Zassenhaus and the lower central series of pro-$p$ groups under a torsion-freeness condition. We also study graph products of (pro-$p$) groups…

Let $X$ be a Weinstein manifold with ideal contact boundary $Y$. If $\Lambda\subset Y$ is a link of Legendrian spheres in $Y$ then by attaching Weinstein handles to $X$ along $\Lambda$ we get a Weinstein cobordism $X_{\Lambda}$ with a…

We define the double ramification hierarchy associated to an F-cohomological field theory and use this construction to prove that the principal hierarchy of any semisimple (homogeneous) flat F-manifold possesses a (homogeneous) integrable…

A 2-web in the plane is given by two everywhere transverse 1-foliations. In this paper we introduce the study of singular 2-webs, given by any two foliations, which may be tangent in some points. We show that such two foliations are tangent…

We show that for $k = 0, 1$ the graph of a continuous mapping $f:D \to \mathbb{R}^k\times\mathbb{C}^p$, defined on a domain $D$ in $\mathbb{C}^n\times\mathbb{R}^k$, is locally foliated by complex $n$-dimensional submanifolds if and only if…

In a talk at the Banff International Research Station in 2015 Asher Auel asked questions about genus one curves in Severi-Brauer varieties $SB(A)$. More specifically he asked about the smooth cubic curves in Severi-Brauer surfaces, that is…

We study a class of holomorphic foliations in (C^3,0) that can be desingularized following the same desingularization chain that a certain quasi-ordinary surface. This intends to be a generalization to the dimension three of the cuspodal…

The notion of a linear deformation of a codimension one foliation into contact structures was introduced in [5]. This concept is a special type of deformation of confoliations. In this paper, we study linear deformations of pairs of…

Deformation of morphisms along leaves of foliations define the tangential foliation on the corresponding space of morphisms. We prove that codimension one fo-liations having a tangential foliation with at least one non-algebraic leaf are…

We consider germs of holomorphic vector fields at the origin of $\mathbb{C}^3$, with non-isolated singularities that are tangent to a holomorphic foliation of codimension one. This configuration is known as a $2$-flag of foliations. The…

Modular data are commonly studied in mathematics and physics. A modular datum defines a finite-dimensional representation of the modular group $SL_2(\mathbb{Z})$. In this paper, we show that there is a one-to-one correspondence between…

Let $\mathcal F$ be a holomorphic one-dimensional foliation on $\mathbb{P}^n$ such that the components of its singular locus $\Sigma$ are curves $C_i$ and points $p_j$. We determine the number of $p_j$, counted with multiplicities, in terms…

The Hecke algebras and quantum group of affine type A admit geometric realizations in terms of complete flags and partial flags over a local field, respectively. Subsequently, it is demonstrated that the quantum group associated to partial…

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,…

Let $\mathcal{F}$ be a transversely orientable codimension one minimal foliation without vanishing cycles of a manifold $M$. We show that if the fundamental group of each leaf of $\mathcal{F}$ has polynomial growth of degree $k$ for some…