Seshadri constants on surfaces of general type

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 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, ...

Remarks on Seshadri Constants

Given a smooth complex projective variety X and an ample line bundle L on X. Fix a point x ∈ X. We consider the question, are there conditions which guarantee the maxima of the Seshadri constant of L at x, i.e ε(L, x) = n √ L? We give a partial answer for surfaces and find examples where the answer to our question is negative. If (X,Θ) is a general principal polarized abelian surface, then ε(Θ,...