Liaison, Schottky Problem and Invariant Theory

Federico Gaeta (1923–2007) was a Spanish algebraic geometer who was a student of Severi. He is considered to be one of the founders of linkage theory, on which he published several key papers. After many years abroad he came back to Spain in the 1980s. He spent his last period as a professor at Universidad Complutense de Madrid. In gratitude to him, some of his personal and mathematically close persons during this last station, all of whom bene?ted in one way or another by his ins- ration, have joined to edit this volume to keep his memory alive. We o?er in it surveys and original articles on the three main subjects of Gaeta’s interest through his mathematical life. The volume opens with a personal semblance by Ignacio Sols and a historical presentation by Ciro Ciliberto of Gaeta’s Italian period. Then it is divided into three parts, each of them devoted to a speci?c subject studied by Gaeta and coordinated by one of the editors. For each part, we had the advice of another colleague of Federico linked to that particular subject, who also contributed with a short survey. The ?rst part, coordinated by E. Arrondo with the advice of R.M.

Federico Gaeta (1923–2007) was a Spanish algebraic geometer who was a student of Severi. He is considered to be one of the founders of linkage theory, on which he published several key papers. After many years abroad he came back to Spain in the 1980s. He spent his last period as a professor at Universidad Complutense de Madrid. In gratitude to him, some of his personal and mathematically close persons during this last station, all of whom bene?ted in one way or another by his ins- ration, have joined to edit this volume to keep his memory alive. We o?er in it surveys and original articles on the three main subjects of Gaeta’s interest through his mathematical life. The volume opens with a personal semblance by Ignacio Sols and a historical presentation by Ciro Ciliberto of Gaeta’s Italian period. Then it is divided into three parts, each of them devoted to a speci?c subject studied by Gaeta and coordinated by one of the editors. For each part, we had the advice of another colleague of Federico linked to that particular subject, who also contributed with a short survey. The ?rst part, coordinated by E. Arrondo with the advice of R.M.

Federico Gaeta.- Federico Gaeta, Among the Last Classics.- Federico Gaeta and His Italian Heritage.- Articles Published by Federico Gaeta.- Linkage Theory.- Gaeta’s Work on Liaison Theory: An Appreciation.- Symmetric Ladders and G-biliaison.- Liaison Invariants and the Hilbert Scheme of Codimension 2 Subschemes in ? n + 2 .- Minimal Links and a Result of Gaeta.- On the Existence of Maximal Rank Curves with Prescribed Hartshorne-Rao Module.- Doubling Rational Normal Curves.- The Schottky Problem.- Survey on the Schottky Problem.- Abelian Solutions of the Soliton Equations and Geometry of Abelian Varieties.- A Special Case of the ?00 Conjecture.- Computation in Algebraic Geometry.- Federico Gaeta: His Last Ten Years of Mathematical Activity.- Covariants Vanishing on Totally Decomposable Forms.- Symmetric Functions and Secant Spaces of Rational Normal Curves.