Title: Linkage and Licci Ideals
Abstract: This talk will first discuss examples, and some history, of linkage and licci ideals. We then give some new results, joint with Claudia Polini and Bernd Ulrich, concerning the structure of licci ideals. Although the history of linkage goes back to the 19th century, we will start with the modern approach of Peskine and Szpiro in 1973; their treatment works well when the base ring is Gorenstein, but in this talk we will only consider the cases of regular local rings or standard graded polynomial rings.
The first part of the talk will give definitions, some examples, discussion of the free resolutions, and some other recent work in codimension 3. The second half will be based on work in progress with Polini and Ulrich. A dream scenario for homogeneous ideals in a polynomial ring would be this: give an algorithm, based solely on the Betti table of the ideal, to determine if an ideal is licci. Can we hope for this dream to be a reality?
