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 ...

In this paper we give a nice formula for the CastelnuovoMumford regularity of the Segre product of modules, under some suitable hypotheses. This extends recent results of David A. Cox, and Evgeny Materov (2009).

We prove an ε-regularity theorem at the endpoint of connected arcs for 2-dimensional Mumford-Shah minimizers. In particular we show that, if in a given ball Br(x) the jump set of a given MumfordShah minimizer is sufficiently close, in the Hausdorff distance, to a radius of Br(x), then in a smaller ball the jump set is a connected arc which terminates at some interior point y0 and it is C 1,α up...

We define the concept of regularity for bigraded modules over a bigraded polynomial ring. In this setting we prove analogs of some of the classical results on m-regularity for graded modules over polynomial algebras.

We extend the “linearly exponential” bound for the Castelnuovo-Mumford regularity of a graded ideal in a polynomial ring K[x1, . . . , xr] over a field (established by Galligo and Giusti in characteristic 0 and recently, by Caviglia-Sbarra for abitrary K) to graded submodules of a graded module over a homogeneous Cohen-Macaulay ring R = ⊕n≥0Rn with artinian local base ring R0. As an application...

I will introduce the notion of Mukai regularity for coherent sheaves on abelian varieties, defined via conditions on the supports of the cohomologies of Fourier-Mukai transform complexes. In a very special form, depending on the choice of a polarization, this resembles and in fact strenghtens the classical notion of Castelnuovo-Mumford regularity. The techniques are in part a generalization of ...