You are cordially invited to the ODTU-Bilkent Algebraic Geometry Seminar.<\/p>\n
Speaker: Hasan Suluyer (ODT\u00dc)<\/p>\n
“Pencils of Conic-Line Curves”<\/p>\n
Abstract: A pencil is a line in the projective space of complex homogeneous polynomials of some degree d > 2. The number m of curves whose irreducible components are only lines in some pencils of degree d curves plays an important role for the existence of special line arrangements, which are called (m,d)-nets. It was proved that the number m, independent of d, cannot exceed 4 for an (m,d)-net. When the degree of each irreducible component of a curve is at most 2, this curve is called a conic-line curve and it is a union of lines or irreducible conics in the complex projective plane. Our main goal is to find an upper bound on the number m of such curves in pencils in CP^2 with the number of concurrent lines in these pencils.<\/p>\n
In this talk, we study the restrictions on the number m of conic-line curves in special pencils. The most general result we obtain is the relation between upper bounds on m and the number of concurrent lines in these pencils. We construct a one-parameter family of pencils such that each pencil in the family contains exactly 4 conic-line curves.<\/p>\n
Date: 25 April 2025, Friday
\nTime: 15:40 (GMT+3)
\nPlace: Zoom<\/p>\n
This is an online seminar. To request the Zoom link, please send a message to sertoz@bilkent.edu.tr<\/p>\n","protected":false},"excerpt":{"rendered":"
You are cordially invited to the ODTU-Bilkent Algebraic Geometry Seminar. Speaker: Hasan Suluyer (ODT\u00dc) “Pencils of Conic-Line Curves” Abstract: A pencil is a line in the projective space of complex homogeneous polynomials of some degree d > 2. The number m of curves whose irreducible components are only lines in [\u2026] <\/p>\n