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Abstract des Vortrages von Davide Veniani

Lines on mildly singular quartics

Counting lines on hypersurfaces has been one of the challenges of algebraic geometers since the Italian school. The fact that on every smooth cubic in the projective space there are exactly 27 lines, combined in a highly symmetrical way, is considered one of the 'gems' of our discipline. In 1943 Beniamino Segre stated correctly that the maximum number of lines on a smooth quartic over an algebraically closed field of characteristic zero is 64, but his proof was wrong. It has recently been corrected by Sławomir Rams and Matthias Schütt using techniques unknown to Segre, such as the theory of elliptic fibrations. The talk will focus on the generalization of these techniques to quartics admitting ADE singularities.