We use functoriality of tropicalization and the geometry of projections of subvarieties of tori to show that the fibers of the tropicalization map are dense in the Zariski topology. For subvarieties of tori over fields of generalized power series, points in each tropical fiber are obtained “constructively” using Kedlaya’s transfinite version of Newton’s method.

Given a finite group G and an abelian variety A acted on by G, to any subgroup H of we associate subvariety AH which the associated Hecke algebra HH for in acts. Any irreducible rational representation W˜ induces natural way. In this paper give equations subvariety. special case these become much easier. We work out some examples.

We have studied the linear codes associated: a) with the surfaces V r−1 2 of order r − 1 of PG(r, q), analyzing in detail the case r = 4; b) with the Schubert subvarieties of the Grassmannian varieties.

Weak Heyting algebras are a natural generalization of Heyting algebras (see [2], [5]). In this work we study certain subvarieties of the variety of weak Heyting algebras in order to extend some known results about compatible functions in Heyting algebras.

A bstract Here we consider what happens when lift a codimension-1 slice of the celestial sphere to bulk spacetime in manner that respects our ability quotient by null generators I ± get codimension-2 hologram. The contour integrals 2D currents for symmetries boundary standard 2-form gauge theory on this novel choice surface and Ward identities follow directly from Noether’s theorem.

We study Stanley decompositions and show that Stanley’s conjecture on Stanley decompositions implies his conjecture on partitionable Cohen-Macaulay simplicial complexes. We also prove these conjectures for all Cohen-Macaulay monomial ideals of codimension 2 and all Gorenstein monomial ideals of codimension 3.

We prove a Sobolev inequality which holds on submanifolds in Euclidean space of arbitrary dimension and codimension. This is sharp if the codimension at most 2 2 </mml:mat...

In [4] the lattice of all subvarieties of the variety G Ex defined by so called externally compatible identities of Abelian groups together with the identity x ≈ y, for any n ∈ N and n ≥ 1 was described. In that paper classes of models of the type (2, 1) where considered. It appears that diagrams of lattices of subvariaties defined by externally compatible identities satisfied in a given equati...

A Schubert class in the Grassmannian is rigid if the only proper subvarieties representing that class are Schubert varieties. The hyperplane class σ1 is not rigid because a codimension one Schubert cycle can be deformed to a smooth hyperplane section. In this paper, we show that this phenomenon accounts for the failure of rigidity in Schubert classes. More precisely, we prove that a Schubert cl...

0. abstract Regarding the resolution of singularities for the differential equations of Painlevé type, there are important differences between the second-order Painlevé equations and those of higher order. Unlike the second-order case, in higher order cases there may exist some meromorphic solution spaces with codimension 2. In this paper, we will give an explicit global resolution of singulari...