On Geometry of Rational Curves on К3 Surfaces

Student: Trapeznikova Olga

Educational Programme: Mathematics (Bachelor)

Final Grade: 10

Year of Graduation: 2016

In this paper we consider K3 surfaces that are complete intersections. It is known, that such surfaces can be divided into three types: nonsingular quartics in P^3, nonsingular intersection of quadric and cubic in P^4 and nonsingular intersection of three quadrics in P^5. It is known, that there are no lines (conics) on the general K3 surface of each type. We prove that varieties of two-dimensional quartics that contain at least one line (conic) are divisors in the the space of all quartic surfaces and calculate the degrees of these divisors. In this paper we also found the number of lines in a pencil of K3 surfaces of the second and the third types.

Full text (added June 14, 2016)

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