A sharp bound for the regularity index of fat points in general position

Abstract

A bound is given for the regularity index of the coordinate ring of a set of fat points in general position in <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="bold upper P Subscript k Superscript n"> <mml:semantics> <mml:msubsup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="bold">P</mml:mi> </mml:mrow> </mml:mrow> <mml:mi>k</mml:mi> <mml:mi>n</mml:mi> </mml:msubsup> <mml:annotation encoding="application/x-tex">{\mathbf {P}}_k^n</mml:annotation> </mml:semantics> </mml:math> </inline-formula> . The bound is attained by points on a rational normal curve.