Combinatorics on Heavy (3,2n+1)-Multinets

Date

2022-06-27

Author

Suluyer, Hasan

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A (k,d)-multinet is a certain configuration of lines and points with multiplicities in CP^2. If there is at least one multiple line in a class of a (k,d)-multinet, it is called heavy. By using the main result proved by Yuzvinsky and the article written by Bassa and Ki¸sisel, we conclude that if a multinet is heavy, the only k value is 3. Therefore, each heavy multinet is of the form (3,d). A heavy (3,2n)-multinet is constructed for n > 1. We discuss the possibilities for combinatorics of lines and points inside a heavy (3,2n+1)-multinet and have showed that there exists neither a heavy (3,3) nor a heavy (3,5)-multinet. Moreover, we have discovered several numerical results of a heavy (3,2n+1)-multinet containing a multiple line consisting of three points from X

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https://hdl.handle.net/11511/107692

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Department of Mathematics, Conference / Seminar