POSTULATION OF ZERO-DIMENSIONAL SCHEMES ON A SMOOTH QUADRIC SURFACE

E Ballico

doi:10.12732/ijpam.v92i4.12

Abstract

Let Q be a smooth quadric surface and Z ⊂ Q a zero-dimensional scheme. We study the postulation of a general union of Z and prescribed numbers of fat points with multiplicity 2 and 3. AMS Subject Classification: 14N05, 14H99

Highlights

Let Q ⊂ P3 be a smooth quadric surface
For each P ∈ Q and any positive integer m the m-point mP is the closed subscheme of Q with (IP )m as its ideal sheaf
Let A ⊂ Q be a general union of e 2-points

Summary

Introduction

Let Q ⊂ P3 be a smooth quadric surface. For each P ∈ Q and any positive integer m the m-point mP is the closed subscheme of Q with (IP )m as its ideal sheaf. A′ ⊂ Q) be a general union of e 2-points and f 3-points Fix zero-dimensional schemes Z ⊂ Q and Z ′ ⊂ Q such that h1 (IZ (c, d)) = 0 and h0 (IZ ′ (c, d)) = 0. 0. Let Z ⊂ Q be a zero-dimensional scheme such that h1 (IZ (c, d)) = 0 and h0 (IZ (c, d − 1)) = 0. Let A ⊂ Q be a general union of e 2-points. 2 for the restrictions on char(K) used in the proofs of some of the statements

Proofs for 2-Points

The Proofs for 3-Points