Related papers: Nakai conjectures for isolated homogeneous hypersu…
The ring $\text{Diff}_{\mathbf{h}}(n)$ of $\mathbf{h}$-deformed differential operators appears in the theory of reduction algebras. In this thesis, we construct the rings of generalized differential operators on the $\mathbf{h}$-deformed…
We study a new class of pseudo differential operators whose symbols satisfy the differential inequality with a mixture of homogeneities. On the other hand, by taking singular integral realization, it can be equivalently defined by kernels…
In this paper we give a positive answer to a question of Nash concerning the arc space of a singularity, for the class of quasi-ordinary hypersurface singularities, extending to this case previous results and techniques of Shihoko Ishii.
We reprove the results of Jordan [18] and Siebert [31] and show that the Lie algebra of polynomial vector fields on an irreducible affine variety X is simple if and only if X is a smooth variety. Given proof is self-contained and does not…
Theorems on the existence of vector fields with given sets of Indexes of isolated Singular points are proved for the cases of closed manifolds, pairs of manifolds, manifolds with boundary, and gradient fields. It is proved that, on a…
We study the weighted spectrum and vanishing cohomology for several classes of isolated hypersurface singularities, and how they contribute to the limiting mixed Hodge structure of a smoothing. Applications are given to several types of…
In Proc Math Sci 129, 70(219), Rakesh Pawar considers and solves a certain extension problem. In this note, we observe that the existence and uniqueness of differential characters (defined as objects which fit into a hexagon diagram) follow…
In this paper we show that any smoothable complex projective variety, smooth in codimension two, with klt singularities and numerically trivial canonical class admits a finite cover, \'etale in codimension one, that decomposes as a product…
The monodromy conjecture is an umbrella term for several conjectured relationships between poles of zeta functions, monodromy eigenvalues and roots of Bernstein-Sato polynomials in arithmetic geometry and singularity theory. Even the…
We show that for a noetherian algebra $A$ whose bounded dg derived category is smooth, the singular Hochschild cohomology (=Tate--Hochschild cohomology) is isomorphic, as a graded algebra, to the Hochschild cohomology of the dg singularity…
Algebraists asked whether or not an operator on the module of smooth sections of the tangent bundle over the commutative ring of smooth functions of a smooth (orientable) manifold (can be any piece of a compact or a complete manifold) can…
This is a second part of alg-geom/9611015. We construct a natural hyperkaehler desingularization for all singular hyperkaehler varieties. The desingularization theorem was proven in alg-geom/9611015 under additional assumption of local…
In 1933, van Kampen described the fundamental groups of the complements of plane complex projective algebraic curves. Recently, Ch\'eniot-Libgober proved an analogue of this result for higher homotopy groups of the complements of complex…
In the objective of studying concentration and oscillation properties of eigenfunctions of the discrete Laplacian on regular graphs, we construct a pseudo-differential calculus on homogeneous trees, their universal covers. We define symbol…
A framework is developed in which one can write down the constraint equations on a three--dimensional hypersurface of arbitrary signature. It is then applied to isolated and dynamical horizons. The derived equations can be used to extract…
Let $k$ be a commutative ring and $A$ a commutative $k$-algebra. In this paper we introduce the notion of enveloping algebra of Hasse--Schmidt derivations of $A$ over $k$ and we prove that, under suitable smoothness hypotheses, the…
This paper shows that Mustata-Nakamura's conjecture holds for pairs consisting of a smooth surface and a multiideal with a real exponent over the base field of positive characteristic. As corollaries, we obtain the ascending chain condition…
The Separatrix Theorem of C. Camacho and P. Sad guarantees the existence of invariant curve (separatrix) passing through the singularity of germ of holomorphic foliation on complex surface, when the surface underlying the foliation is…
Differential calculus on discrete sets is developed in the spirit of noncommutative geometry. Any differential algebra on a discrete set can be regarded as a `reduction' of the `universal differential algebra' and this allows a systematic…
We show that a Hodge class of a complex smooth projective hypersurface is an analytic logarithmic De Rham class. On the other hand we show that for a complex smooth projective variety an analytic logarithmic De Rham class of of type $(d,d)$…