[Turkmath:5287] Symbolic Computation Istanbul Meetings

[Zafeirakis Zafeirakopoulos]

Dear colleagues,

The next Symbolic Computation Istanbul Meeting (SCIM) will take place this
Friday at 17:00 in IMBM. The talk will also be available in zoom.

If you wish to receive SCIM announcements and the zoom link, please fill in
this form: https://tinyurl.com/symbolicmeetings/

Friday December 3,  17:00
Title: The smooth cubic surfaces with 15 lines
Speaker: Dr. Fatma Karaoğlu (Department of Mathematics, Tekirdag Namik
Kemal University, Turkey)

Abstract
It is well-known that a smooth cubic surface has 27 lines over an
algebraically closed field. If the field is not closed, however, fewer
lines are possible. The next possible case is that of smooth cubic surfaces
with 15 lines. This work is a contribution to the problem of classifying
smooth cubic surfaces with 15 lines over fields of positive characteristic.
We present an algorithm to classify such surfaces over small finite fields.
Our classification algorithm is based on a new normal form of the equation
of a cubic surface with 15 lines and at most 10 Eckardt points. The case of
cubic surfaces with more than 10 Eckardt points is dealt with separately.
Classification results for fields of order at most 13 are presented and a
verification using an enumerative formula of Das is performed. Our work is
based on a generalization of the old result due to Cayley and Salmon that
there are 27 lines if the field is algebraically closed. Along the way, we
show that the line-intersection graph of smooth cubic surfaces with 15
lines is unique.

Best regards,
Zafeirakis Zafeirakopoulos
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