Cayley octads, plane quartic curves, Del Pezzo surfaces of degree 2 and double Veronese cones

Jihun Park (POSTECH)

21-Jul-2020, 11:00-12:00 (4 years ago)

Abstract: 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 this talk, we set up a one-to-one correspondence between isomorphism classes of smooth plane quartic curves and isomorphism classes of double Veronese cones with 28-singular points. Also, we explain how the 36 even theta characteristics of a given smooth quartic curve appear in the corresponding double Veronese cone. This is a joint work with Hamid Ahmadinezhad, Ivan Cheltsov and Constantin Shramov.

algebraic geometry

Audience: researchers in the topic


ZAG (Zoom Algebraic Geometry) seminar

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Organizers: Jesus Martinez Garcia*, Ivan Cheltsov*, Jungkai Chen, Jérémy Blanc, Ernesto Lupercio, Yuji Odaka, Zsolt Patakfalvi, Julius Ross, Cristiano Spotti, Chenyang Xu
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