Related papers: An introduction to $V$-filtrations

Recently M. Mustata and V. Srinivas related a natural conjecture about the Frobenius action on the cohomology of the structure sheaf after reduction to characteristic $p > 0$ with another conjecture connecting multiplier ideals and test…

Let $f:\mathbb{C}^{n+1} \to \mathbb{C}$ be a germ of hypersurface with isolated singularity. One can associate to $f$ a polarized variation of mixed Hodge structure $\mathcal{H}$ over the punctured disc, where the Hodge filtration is the…

Contents 1. Algebraicity criterion: statement 2. Proof of the algebraicity criterion. 3. Pseudoeffectivity and movable classes. 4. Harder-Narasimhan filtrations and pseudo-effectivity. 5. Pseudo-effectivity of relative canonical bundles. 6.…

Let G be a reductive algebraic group over a field k. When k=C, R.K.Brylinski constructed a filtration of weight spaces of a G module, using the action of a principal nilpotent element of the Lie algebra, and proved that this filtration…

This is a note to revisit interesting results of H. Esnault, C. Sabbah, M. Saito and J.-D. Yu on the Kontsevich complexes from the viewpoint of mixed twistor D-modules. We explicitly describe the V-filtration of the mixed twistor D-modules…

The first part of this paper is a review of the Strominger-Yau-Zaslow conjecture in various settings. In particular, we summarize how, given a pair (X,D) consisting of a Kahler manifold and an anticanonical divisor, families of special…

We review recent progress concerning the analysis of Lagrangians on immersions into $\mathbb{R}^d$ depending on the first and second fundamental forms and their covariant derivatives.

We construct differential equivariant K-theory of representable smooth orbifolds as a ring valued functor with the usual properties of a differential extension of a cohomology theory. For proper submersions (with smooth fibres) we construct…

This is Part II of the series of our papers under the title "Toward resolution of singularities over a field of positive characteristic (The Idealistic Filtration Program)". See http://arxiv.org/abs/math/0607009 for Part I.

We investigate the geometry of holomorphic curves and complex surfaces from the perspective of singularity theory. We show that, with a suitable choice of a complex bilinear symmetric form, the families of functions and mappings that…

Let $K$ be a field of characteristic zero, $X$ and $Y$ be smooth $K$-varieties, and let $V$ be a finite dimensional $K$-vector space. For two algebraic morphisms $\varphi:X\rightarrow V$ and $\psi:Y\rightarrow V$ we define a convolution…

This is a short introduction to the study of compactifications of F-theory on elliptic Calabi-Yau threefolds near colliding singularities. In particular we consider the case of non-transversal intersections of the singular fibers.

We generalize the BV formalism for the physical theories on supermanifolds with graded symmetry algebras realized off-shell and on-shell. An application of such generalization to supersymmetric theories allows us to formulate the new…

Let $\mathbb{K}$ be an algebraically closed field, and $A \subset \mathbb{K}[x_{1}, \ldots, x_n]$ be a subalgebra of finite codimension. It is known that there exists a (not necessarily unique) finite filtration of $\mathbb{K}$-algebras \[…

We develop the theory of Hodge ideals for Q-divisors by means of log resolutions, extending our previous work on reduced hypersurfaces. We prove local (non-)triviality criteria and a global vanishing theorem, as well as other analogues of…

In this paper, we mainly build up the theory of sheaf-correspondence filtered spaces and stratified de Rham complexes for studying singular spaces. We prove the finiteness of a stratified de Rham cohomology and obtain its isomorphism to…

We explore connections between geometric properties of the Levi foliation of a Levi-flat hypersurface M and holomorphic convexity of compact sets in M, or bounded in part by M. Applications include extendability of Cauchy-Riemann functions,…

This is a mostly expository paper, intended to explain a very natural relationship between two a priori distinct notions appearing in the literature: Generic Vanishing in the context of vanishing theorems and birational geometry, and…

We study the local geometry of the pullback of a variety via a finite holomorphic map. In particular, we are looking for properties of $V = F^{-1}(W)$ such that if $V$ has the property $A$, then $W$ must have the property $A$. We show that…

In this paper we generalize some results by Siersma, Pellikaan, and de Jong regarding morsifications of singular hypersurfaces whose singular locus is a smooth curve, and present some applications to the study of Yomdin-type isolated…