Seshadri constants on surfaces with Picard number 1

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...

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 on Rational Surfaces with Anticanonical Pencils

We provide an explicit formula for Seshadri constants of any polarizations on rational surfaces X such that dim |−KX | ≥ 1. As an application, we discuss relationship between singularities of log del Pezzo surfaces and Seshadri constants of their anticanonical divisors. We also give some remarks on higher order embeddings of del Pezzo surfaces.

Seshadri Constants in a Family of Surfaces

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, ...