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Olivier Martin: Measures of association for algebraic varieties

Tid: To 2021-12-09 kl 14.00 - 15.00

Plats: Institut Mittag-Leffler, Seminar Hall Kuskvillan (alt. Zoom, meeting ID: 921 756 1880)

Medverkande: Olivier Martin (Stony Brook University)

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Abstract: I will discuss recent work in collaboration with R. Lazarsfeld which explores the following question: Given varieties X and Y of the same dimension how far are they from being birational? I will define various "measures of association" which quantify the failure of X and Y to be birational and present partial results, heuristics, and several open problems. For instance, given an n-fold Z dominating very general hypersurfaces X and Y in \(\mathbb{P}^{n+1}\) of degrees \(d,e>2n+1\), we show that the degrees of the projections \(Z\to X\) and \(Z\to Y\) are at least d and e. Moreover, given very general hyperelliptic curves X and Y, any hyperelliptic curve in \(X\times Y\) is contracted by the projection to X or the projection to Y.