Related papers: Mather-Yau Theorem in Positive Characteristic

While the classification of univariate power series up to coordinate change is trivial in characteristic 0, this classification is very different in positive characteristic. In this note we give a complete classification of univariate power…

We show that every convergent power series with monomial extended Jacobian ideal is right equivalent to a Thom-Sebastiani polynomial. This solves a problem posed by Hauser and Schicho. On the combinatorial side, we introduce a notion of…

Consider the ring of holomorphic function germs in $C^n$ and denote by $M$ the maximal ideal of this ring. For any a holomorphic function germ $f$ with an isolated critical point, the finite determinacy theorem (Mather-Tougeron) asserts…

In this note, We proved that a compact Sasakian manifold $( M, {\xi}, {\eta}, {\Phi} , g )$ with negative transverse holomorphic sectional curvature must have has a Sasakian structure $( {\xi}, {\eta} , {\Phi} , g )$ with negative…

We compute the motivic Euler characteristic of Ayoub's nearby cycles spectrum in terms of strata of a semi-stable reduction, for a degeneration to multiple semi-quasi-homogeneous singularities. This allows us to compare the local picture at…

In light of Sen's weak coupling limit of F-theory as a type IIB orientifold, the compatibility of the tadpole conditions leads to a non-trivial identity relating the Euler characteristics of an elliptically fibered Calabi-Yau fourfold and…

For tame arbitrary-length toral, also called positive regular, supercuspidal representations of a simply connected and semisimple $p$-adic group $G$, constructed as per Adler-Yu, we determine which components of their restriction to a…

We study classical invariants for plane curve singularities $f\in K[[x,y]]$, $K$ an algebraically closed field of characteristic $p\geq 0$: Milnor number, delta invariant, kappa invariant and multiplicity. It is known, in characteristic…

Twisted Calabi-Yau algebras are a generalisation of Ginzburg's notion of Calabi-Yau algebras. Such algebras A come equipped with a modular automorphism \sigma \in Aut(A), the case \sigma = id being precisely the original class of Calabi-Yau…

We consider the homotopical dynamics on compact orientable surfaces of positive genus g. We establish a sufficient and necessary algebraic criterion for homotopy classes with infinitely many periodic points of maps on such surfaces in terms…

The main theorem (2.2) consists in two characterizations of isomorphisms of factorial domains in terms of prime or primary rings elements, and unramified, flat or weakly injective affine schemes morphisms. In order to apply this theorem to…

In this paper, we show that weakly symmetric $\tau$-tilting finite algebras have positive definite Cartan matrices, which implies that we can prove $\tau$-tilting infiniteness of weakly symmetric algebras by calculating their Cartan…

A T-variety is an algebraic variety X with an effective regular action of an algebraic torus T. Altmann and Hausen gave a combinatorial description of an affine T-variety X by means of polyhedral divisors. In this paper we compute the…

Let $\phi$ be a positive unital normal map of a von Neumann algebra $M$ into itself, and assume there is a family of normal $\phi$-invariant states which is faithful on the von Neumann algebra generated by the image of $\phi$. It is shown…

We study deformations of rational curves and their singularities in positive characteristic. We use this to prove that if a smooth and proper surface in positive characteristic $p$ is dominated by a family of rational curves such that one…

We say a mirror pair of Calabi-Yau varieties exhibits strong arithmetic mirror symmetry if the number of points on each variety over a finite field is equivalent, modulo the order of that field. We search for strong mirror symmetry in…

For an ordinary K3 surface over an algebraically closed field of positive characteristic we show that every automorphism lifts to characteristic zero. Moreover, we show that the Fourier-Mukai partners of an ordinary K3 surface are in…

The paper contains a proof that elliptic genus of a Calabi-Yau manifold is a Jacobi form, finds in which dimensions the elliptic genus is determined by the Hodge numbers and shows that elliptic genera of a Calabi-Yau hypersurface in a toric…

An abelian variety defined over an algebraically closed field k of positive characteristic is supersingular if it is isogenous to a product of supersingular elliptic curves and is superspecial if it is isomorphic to a product of…

We define the notion of isosingular loci of algebraic varieties, following the analytic case first studied by Ephraim. In particular, we give a partial extension of his main result in arbitrary characteristic and a full extension assuming…