일시: 2020.11.06(금) 오후5시
Zoom: https://yonsei.zoom.us/j/96321962020
제목: Cayley octads, plane quartic curves, Del Pezzo surfaces of degree 2, and double Veronese cones
연사: 박지훈 (교수,포항공대 수학과)
초록: A net of quadrics in the 3-dimensional projective space whose singular members are parametrized by a smooth plane quartic curve has exactly
eight distinct base points, called a regular Cayley octad. It is a classical result that there is a one-to-one correspondence between isomorphism
classes of regular Cayley octads and isomorphism classes of smooth plane quartic curves equipped with even theta-characteristics. We can
also easily observe a one-to-one correspondence between isomorphism classes of smooth plane quartic curves and isomorphism classes of
smooth Del Pezzo surfaces of degree 2. In my talk, I will set up a oneto-one correspondence between isomorphism classes of smooth plane
quartic curves and isomorphism classes of double Veronese cones with 28-singular points. Also, I will explain how the 36 even theta
characteristics of a given smooth quartic curve appear in the corresponding double Veronese cone.