Nov 05, 2020
Thursday

12:00 PM  02:00 PM


Fellowship of the Ring, National Seminar: CalabiYau threefolds in P^n and Gorenstein rings
Henry Schenck (Auburn University)

 Location
 MSRI: Online/Virtual
 Video

 Abstract
To attend this seminar, you must register in advance, by clicking HERE.
Paper here:
http://arxiv.org/abs/2011.10871
Abstract:
A projectively normal CalabiYau threefold $X \subseteq \mathbb{P}^n$ has an ideal $I_X$ which is arithmetically Gorenstein, of CastelnuovoMumford regularity four. Such ideals have been intensively studied when $I_X$ is a complete intersection, as well as in the case were $X$ has codimension three. In the latter case, the BuchsbaumEisenbud theorem shows that $I_X$ is given by the Pfaffians of a skewsymmetric matrix. A number of recent papers study the situation when $I_X$ has codimension four. We prove there are 16 possible betti tables for an arithmetically Gorenstein ideal I with codim(I) = 4 = regularity(I), and that 9 of these arise for prime nondegenerate threefolds. We investigate the situation in codimension five or more, obtaining examples of X with $h^{p,q}(X)$ not among those appearing for $I_X$ of lower codimension or as complete intersections in toric Fano varietiesin other words, CalabiYau's with Hodge numbers not previously known to occur. A main feature of our approach is the use of inverse systems to identify possible betti tables for X. This is joint work with M. Stillman, B. Yuan.
 Supplements



