BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Henry Schenck (Auburn University) DTSTART:20201105T200000Z DTEND:20201105T213000Z DTSTAMP:20260423T021400Z UID:FOTR/29 DESCRIPTION:Title: Ca labi-Yau threefolds in P^n and Gorenstein rings\nby Henry Schenck (Aub urn University) as part of Fellowship of the Ring\n\n\nAbstract\nA project ively normal Calabi-Yau threefold $X \\subseteq \\mathbb{P}^n$ has an idea l $I_X$ which is arithmetically Gorenstein\, of Castelnuovo-Mumford regula rity four. Such ideals have been intensively studied when $I_X$ is a compl ete intersection\, as well as in the case were $X$ has codimension three. In the latter case\, the Buchsbaum-Eisenbud theorem shows that $I_X$ is gi ven by the Pfaffians of a skew-symmetric matrix. A number of recent papers study the situation when $I_X$ has codimension four. We prove there are 1 6 possible betti tables for an arithmetically Gorenstein ideal I with codi m(I) = 4 = regularity(I)\, and that 9 of these arise for prime nondegenera te 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 varie ties--in other words\, Calabi-Yau's with Hodge numbers not previously know n to occur. A main feature of our approach is the use of inverse systems t o identify possible betti tables for X. This is joint work with M. Stillma n and B. Yuan\n LOCATION:https://researchseminars.org/talk/FOTR/29/ END:VEVENT END:VCALENDAR