BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Lisa Marquand (Stony Brook University) DTSTART:20201109T210000Z DTEND:20201109T220000Z DTSTAMP:20260423T021243Z UID:AGSAGS/8 DESCRIPTION:Title: H yperplane sections and Moduli\nby Lisa Marquand (Stony Brook Universit y) as part of American Graduate Student Algebraic Geometry Seminar\n\n\nAb stract\nOne way to produce new varieties from a fixed subvariety of projec tive space is to intersect with linear subspaces. When we consider a cubic threefold $X$ in $\\mathbb{P}^4$\, we can consider hyperplane sections: t o every hyperplane (considered as a point in the dual projective space) we can associate a cubic surface namely the intersection $X \\cap H$. One na tural question is to ask\, given a cubic surface $Y$\, how many times does it appear as a hyperplane section of $X$ (up to projective equivalence)? More rigorously\, we can define a rational map which takes a hyperplane $H $ to the class of the intersection\, considered as a point in the moduli s pace of cubic surfaces (GIT). One can check that this is a generically fin ite surjective map\, and thus answering our question is equivalent to calc ulating the degree of this map. Although the question is enumerative\, the techniques involved are particularly interesting: the wonderful blow-up t echnique of De Concini-Procesi\, plus the dual perspective of the moduli o f cubic surfaces. This is a work in progress\, and we will actually consid er a slight modification resulting in easier computations.\n LOCATION:https://researchseminars.org/talk/AGSAGS/8/ END:VEVENT END:VCALENDAR