»ã±¨±êÌâ (Title)£ºBezout, Cayley-Bacharach, and associativity of the group action on an elliptic curve (Bezout¶¨Àí¡¢Cayley-Bacharach¶¨Àí
£¬ÒÔ¼°ÍÖÔ²ÇúÏßÉÏȺ×÷ÓõĽáºÏÂÉ)

»ã±¨ÈË (Speaker)£º Peter van der Kamp ½ÌÊÚ£¨La Trobe University, Australia£©

»ã±¨¹¦·ò (Time)£º2024Äê09ÔÂ25ÈÕ(ÖÜÈý) 15:30-17:00

»ã±¨µØÖ· (Place)£ºÐ£±¾²¿GJ303

Ô¼ÇëÈË(Inviter)£ºÕÅÐÛʦ ½ÌÊÚ

Ö÷°ì²¿ÃÅ£ºÀíѧԺÊýѧϵ

»ã±¨ÌáÒª£º

I will state Bezout¡¯s theorem, and will explain how to determine the multiplicity of a point in the intersection of two plane curves (a la Fulton). I will then provide a geometric proof of the Cayley-Bacharach theorem, which is (only) based on Bezout¡¯s theorem, and linear algebra. Some consequences are Pappus¡¯s theorem, Pascal¡¯s theorem, and the associativity of the group action on an elliptic curve.