An ind-variety is an inductive limit of closed embeddings algebraic varieties and ind-group a group object in the category ind-varieties. These notions were first introduced by Shafarevich study automorphism affine spaces have been studied many authors afterwards. ind-torus obtained as tori that are also homomorphisms. In this paper, we introduce natural definition toric ind-varieties having op...

We consider solutions of affine stochastic functional differential equations on R. The drift of these equations is specified by a functional defined on a general function space B which is only described axiomatically. The solutions are reformulated as stochastic processes in the space B. By representing such a process in the bidual space of B we establish that the transition functions of this p...

We introduce a cap product pairing for homology and cohomology of tropical cycles on integral affine manifolds with singularities. show the is perfect over $\mathbb{Q}$ in degree one when manifold has at worst symple By joint work Siebert, computes period integrals its perfectness implies versality canonical Calabi-Yau degenerations. also give an intersection theoretic application Strominger-Ya...

Abstract Let $${\mathcal {C}} \subset {\mathbb {N}}^p$$ C ⊂ N p be a finitely generated integer cone and $$S\subset {\mathcal {C}}$$ S an affine semigroup such that the real cones by S are equal. ...

Let C ⊂ N be an affine semigroup, and R = K[C] its semigroup ring. This paper is a collection of various results on “C-graded” R-modules M = ⊕ c∈C Mc, especially, monomial ideals of R. For example, we show the following: If R is normal and I ⊂ R is a radicalmonomial ideal (i.e., R/I is a generalization of Stanley-Reisner rings), then the sequentially Cohen-Macaulay property of R/I is a topologi...

We consider the Noetherian properties of the ring of differential operators of an affine semigroup algebra. First we show that it is always right Noetherian. Next we give a condition, based on the data of the difference between the semigroup and its scored closure, for the ring of differential operators being anti-isomorphic to another ring of differential operators. Using this, we prove that t...

We build two toric embedded resolutions procedures of a reduced quasiordinary hypersurface singularity (S, 0) of dimension d . The first one provides an embedded resolution as hypersurface of (C, 0) as a composition of toric morphisms which depend only on the characteristic monomials associated to a quasi-ordinary projection (S, 0) → (C, 0) . This gives a positive answer to a a question of Lipm...

We show that monomial ideals generated in degree two satisfy a conjecture by Eisenbud, Green and Harris. In particular we give a partial answer to a conjecture of Kalai by proving that h-vectors of flag Cohen-Macaulay simplicial complexes are h-vectors of Cohen-Macaulay balanced simplicial complexes.

We study topological rigidity of algebraic dynamical systems. In the first part of this paper we give an algebraic condition for rigidity that unifies previous rigidity results and we settle an old question of Walters. In the second part we consider the rigidity of hyperbolic systems. An algebraic dynamical system (X, S) has a phase space X that is a compact abelian group and a transformation s...