1 Dipartimento di Matematica “Guido Castelnuovo”, SAPIENZA Università di Roma, P.le A. Moro, 2, I-00185 Roma, Italy. E-mail: [email protected]. Research supported by a grant from SAPIENZA Università di Roma. 2 Dipartimento di Matematica “Guido Castelnuovo”, SAPIENZA Università di Roma, P.le A. Moro, 2, I-00185 Roma, Italy. E-mail: [email protected]. 3 Department of Mathematic...

This paper characterizes the Castelnuovo-Mumford regularity by evaluating the initial ideal with respect to the reverse lexicographic order.

This paper characterizes the Castelnuovo-Mumford regularity by evaluating the initial ideal with respect to the reverse lexicographic order.

Abstract We call a smooth irreducible projective curve Castelnuovo if it admits birational map into the r-space such that image has degree at least 2r+1 and maximum possible geometric genus (which one can calculate by classical formula due to Castelnuovo). It is well known must lie on Hirzebruch surface (rational ruled surface). Conversely, making use of result W. Castryck F. Cools concerning s...

Bounds for the Castelnuovo-Mumford regularity and Hilbert coefficients are given in terms of the arithmetic degree (if the ring is reduced) or in terms of the defining degrees. From this it follows that there exists only a finite number of Hilbert functions associated with reduced algebras over an algebraically closed field with a given arithmetic degree and dimension. A good bound is also give...

Abstract. The classical Castelnuovo numbers count linear series of minimal degree and fixed dimension on a general curve, in the case when this number is finite. For pencils, that is, linear series of dimension one, the Castelnuovo numbers specialize to the better known Catalan numbers. Using the Fulton-Pragacz determinantal formula for flag bundles and combinatorial manipulations, we obtain a ...

We develop a multigraded variant of Castelnuovo-Mumford regularity. Motivated by toric geometry, we work with modules over a polynomial ring graded by a finitely generated abelian group. As in the standard graded case, our definition of multigraded regularity involves the vanishing of graded components of local cohomology. We establish the key properties of regularity: its connection with the m...

This paper gives explicit formulas for the reduction number and Castelnuovo–Mumford regularity of projective monomial curves.