相关论文: Singularities of dual varieties in characteristic …

We study the singularities of the projective dual variety.

We study Coble surfaces in characteristic 2, in particular, singularities of their canonical coverings. As an application we classify Coble surfaces with finite automorphism group in characteristic 2. There are exactly 9 types of such…

We give an overview of invariants of algebraic singularities over perfect fields. We then show how they lead to a synthetic proof of embedded resolution of singularities of 2-dimensional schemes.

A theory of characteristic classes of vector bundles and smooth manifolds plays an important role in the theory of smooth manifolds. An investigation of reasonable notions of characteristic classes of singular spaces started since a…

It is given the diffeomorphism classification on generic singularities of tangent varieties to curves with arbitrary codimension in a projective space. The generic classifications are performed in terms of certain geometric structures and…

This text is a draft of the review paper on projectively dual varieties. Topics include dual varieties, Pyasetskii pairing, discriminant complexes, resultants and schemes of zeros, secant and tangential varieties, Ein theorems, applications…

For a weighted quasihomogeneous two dimensional hypersurface singularity, we define a smoothing with unipotent monodromy and an isolated graded normal singularity. We study the natural weighted blow up of both the smoothing and the surface.…

We study the behavior of Du~Bois singularities under base change and fiber products. For embeddable varieties in characteristic zero, we show that Du~Bois singularities descend from any field extension. We also prove that the product of a…

We consider a planar dynamical system generated by two stable linear vector fields with distinct fixed points and random switching between them. We characterize singularities of the invariant density in terms of the switching rates and…

Looking in positive characteristic for failures of the Bertini-Sard theorem, we determine, up to birational equivalence, the separable proper morphisms of smooth algebraic varieties in characteristic two, whose fibres are non-smooth curves…

We construct a modular desingularisation of $\overline{\mathcal{M}}_{2,n}(\mathbb{P}^r,d)^{\text{main}}$. The geometry of Gorenstein singularities of genus two leads us to consider maps from prestable admissible covers: with this enhanced…

We study sheaves of differential forms and their cohomology in the h-topology. This allows to extend standard results from the case of smooth varieties to the general case. As a first application we explain the case of singularities arising…

We study singularities obtained by the contraction of the maximal divisor in compact (non kaehlerian) surfaces which contain global spherical shells. These singularities are of genus 1 or 2, may be Q-Gorenstein, numerically Gorenstein or…

This is a survey on recent results regarding singularities that occur on higher dimensional stable varieties.

This note discusses some examples showing that the crystalline cohomology of even very mildly singular projective varieties tends to be quite large. In particular, any singular projective variety with at worst ordinary double points has…

We study the singularities of secant varieties of smooth projective varieties using methods from birational geometry when the embedding line bundle is sufficiently positive. More precisely, we study the Du Bois complex of secant varieties…

Consider a smooth projective curve and a given embedding into projective space via a sufficiently positive line bundle. We can form the secant variety of $k$-planes through the curve. These are singular varieties, with each secant variety…

In this paper, we classify the configurations of the singular points which appear on the quotients of the projective plane by the $1$-foliations of degree $-1$ in characteristic $2$.

We consider characterizations of projective varieties in terms of their tangents. S. Mori established the characterization of projective spaces in arbitrary characteristic by ampleness of tangent bundles. J. Wahl characterized projective…

We give a method to construct explicitly a supersingular curve of given genus g in characteristic 2.