A subcube partition is a of the Boolean cube $\{0,1\}^n$ into subcubes. irreducible if only sub-partitions whose union are singletons and entire partition. tight it “mentions” all coordinates.
 We study extremal properties partitions: minimal size, weight, maximal number points, minimum dimension. also consider existence homogeneous partitions, in which subcubes have same dimensions. addit...

In this paper, we give two applications of the theory of multiplier ideals to vector bundles over complex projective manifolds, generalizing to higher rank results already established for line bundles. The first addresses the existence of sections of (suitable twists) of symmetric powers of a very ample vector bundle, vanishing on a given subvariety. The second is a vanishing theorem of Gri‰ths...

The Schubert cells eλ are the orbits of the Iwahori subgroup B̃, while the Birkhoff strata Sλ are the orbits of the opposite Iwahori subgroup B̃ . The cells and the strata are dual in the sense that Sλ ∩ eλ = {λ}, and the intersection is transverse. The closure of eλ is the affine Schubert variety Xλ. It has dimension l (λ), where l is the minimal length occuring in the coset λW̃I , and its cells ...

Let Y0(p) be the Drinfeld modular curve parameterizing Drinfeld modules of rank two over Fq[T ] of general characteristic with Hecke level p-structure, where p ⊳ Fq[T ] is a prime ideal of degree d. Let J0(p) denote the Jacobian of the unique smooth irreducible projective curve containing Y0(p). Define N(p) = q−1 q−1 , if d is odd, and define N(p) = q −1 q2−1 , otherwise. We prove that the tors...

Globally, the solution set of a system of polynomial equations with complex coefficients can be decomposed into irreducible components. Using numerical algebraic geometry, each irreducible component is represented using a witness set thereby yielding a numerical irreducible decomposition of the solution set. Locally, the irreducible decomposition can be refined to produce a local irreducible de...