Addendum: a Complex Surface of General Type

A Complex Surface of General Type

This paper is an addendum to [2]. In this paper we construct a minimal complex surface of general type with pg = 0, K 2 = 2 and H1 = Z2 using a rational blow-down surgery and Q-Gorenstein smoothing theory. Since all the proofs except H1 = Z2 are basically the same as the proofs of the main construction in [2], we only explain how to construct such a surface and then we show that the surface has...

Heesang Park, Jongil Park and Dongsoo Shin

This paper is an addendum to [4], in which the authors constructed a simply connected minimal complex surface of general type with pg = 0 and K 2 = 3. Motivated by Y. Lee and the second author’s recent construction on a surface of general type with pg = 0, K 2 = 2 and H1 = Z/2Z [3], we extend the result to the K = 3 case in this paper. That is, we construct a new non-simply connected minimal su...

Addendum to: "Infinite-dimensional versions of the primary, cyclic and Jordan decompositions", by M. Radjabalipour

In his paper mentioned in the title, which appears in the same issue of this journal, Mehdi Radjabalipour derives the cyclic decomposition of an algebraic linear transformation. A more general structure theory for linear transformations appears in Irving Kaplansky's lovely 1954 book on infinite abelian groups. We present a translation of Kaplansky's results for abelian groups into the terminolo...

An improved bound for the degree of smooth surfaces in P not of general type

This is an addendum to the paper of Braun and Fløystad ([BF]) on the bound for the degree of smooth surfaces in P 4 not of general type. (In fact, any statements made here without comment will be found there.) Using their construction and the regularity of curves in P 3 , one may lower the bound a little more. We will prove the following: Theorem. Let S be a smooth surface of degree d in P 4 no...

Addendum To: Shape Constraints and Optimal Bases for C Hermite Interpolatory Subdivision Schemes