This paper is concerned with a relationship between the existence of subvarieties of principally polarized abelian varieties (ppav’s) having minimal cohomology class and the (generic) vanishing of certain sheaf cohomology, based on the Generic Vanishing criterion studied in [PP3]. This is in analogy with the well-known equivalence between a subvariety in projective space being of minimal degree...

To any d-web of codimension one on a holomorphic n-dimensional manifold M (d > n), we associate an analytic subset S of M . We call ordinary the webs for which S has a dimension at most n− 1 or is empty. This condition is generically satisfied. We prove that the rank of a ordinary d-web has an upper-bound π′(n, d) which, for n ≥ 3, is strictly smaller than the bound π(n, d) of Castelnuovo. This...

Let ρC be the regularity of the Hilbert function of a projective curve C in P K over an algebraically closed field K and α1, . . . , αn−1 be minimal degrees for which there exists a complete intersection of type (α1, . . . , αn−1) containing the curve C. Then the Castelnuovo-Mumford regularity of C is upper bounded by max{ρC +1, α1 + . . .+αn−1 − (n− 2)}. We study and, for space curves, refine ...

Abstract Let $$A=\{a_0,\ldots ,a_{n-1}\}$$ A = { a 0 , … n - 1 } be a finite set of $$n\ge 4$$...

We give an explicit formula for the degree of Grothendieck polynomial a Grassmannian permutation and closely related Castelnuovo-Mumford regularity Schubert determinantal ideal permutation. then provide counterexample to conjecture Kummini-Lakshmibai-Sastry-Seshadri on regularities standard open patches particular varieties show that our work gives rise alternate in these cases. end with new <i...