Seshadri constants and surfaces of minimal degree

Seshadri constants on algebraic surfaces

0. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. Seshadri constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2. Very ample line bundles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3. Bounds on global Seshadri constants . . . . . . . . . . . . . . . . . . . . . . . . 9 4. The degree of sub-maximal cu...

Seshadri constants and the geometry of surfaces

This numerical definition is equivalent to a more intuitive geometric definition. In particular, ǫ(x,A) is the supremum of all non–negative rational numbers α such that the linear series |nA| separates nα–jets at x for n sufficiently large and divisible. Note that if L is a nef line bundle on X then Definition 1 still makes sense and ǫ(x, L) is defined accordingly. When L is nef but not ample, ...

Seshadri Constants in a Family of Surfaces

Computing Seshadri Constants on Smooth Toric Surfaces

Abstract. In this paper we compute the Seshadri constants at the general point on many smooth polarized toric surfaces. We consider the case when the degree of jet separation is small or the core of the associated polygon is a line segment. Our main result is that in this case the Seshadri constant at the general point can often be determined in terms of easily computable invariants of the surf...

Seshadri constants and very ample divisors on algebraic surfaces

A broadly applicable geometric approach for constructing nef divisors on blow ups of algebraic surfaces at n general points is given; it works for all surfaces in all characteristics for any n. This construction is used to obtain substantial improvements for currently known lower bounds for n point Seshadri constants. Remarks are included about a range of applications to classical problems invo...