Seshadri constants and very ample divisors on algebraic surfaces
By Brian Harbourne. 2001
48 citations recorded by the source corpus.
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 involving linear systems on P2.
Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/f0ae4dfe2873fd82d098e8f82cb8fd76da5f9284
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In Algebra and Number Theory
In Computational Theory and Mathematics
In Geometry and Topology
Citations in the corpus
- Comparing powers and symbolic powers of ideals (2007, methodology): “This suggests, more generally, to look at the set of N-wise intersections of s ≥ N + 1 general hyperplanes in PN. More generally yet, for 1 ≤ e ≤ N and s ≥ e, let SN(e,s, d) denote the reduced scheme consisting of the e-wise intersections of s general hypersurfaces H1 ,...,Hs in PN of respective de”
- Linear systems with multiple base points in P2 (2001, background): “2; then for m large enough the bound from Theorem I.3(c) is α(n;m) ≥ 1 + ⌊(mr + g − 1)/d⌋. This is better than the bound of Corollary IV.1.1.2 of [H4] (which generalizes the main theorem of [H3]; see [H5] for further generalizations and related results), which is just α(n;m) ≥ mr/d. On the other han”