Using tropical degenerations for proving the nonexistence of certain nets

Güntürkün, Mustafa Hakan
A net is a special configuration of lines and points in the projective plane. There are certain restrictions on the number of its lines and points. We proved that there cannot be any (4,4) nets in CP^2. In order to show this, we use tropical algebraic geometry. We tropicalize the hypothetical net and show that there cannot be such a configuration in CP^2.


An obstruction to finding algebraic models for smooth manifolds with prescribed algebraic submanifolds
CELIKTEN, A; Ozan, Yıldıray (2001-03-01)
Let N ⊆ M be a pair of closed smooth manifolds and L an algebraic model for the submanifold N. In this paper, we will give an obstruction to finding an algebraic model X of M so that the submanifold N corresponds in X to an algebraic subvariety isomorphic to L.
A formula for the joint local spectral radius
Emel'yanov, EY; Ercan, Z (American Mathematical Society (AMS), 2004-01-01)
We give a formula for the joint local spectral radius of a bounded subset of bounded linear operators on a Banach space X in terms of the dual of X.
A remark on CD0(K)-spaces
Alpay, S.; Ercan, Z. (Springer Science and Business Media LLC, 2006-05-01)
A representation of the CDo (K)-space is given in [1, 2] for a compact Hausdorff space K without isolated points. We generalize this to an arbitrary countably compact space K without any assumption on isolated points.
On a Fitting length conjecture without the coprimeness condition
Ercan, Gülin (Springer Science and Business Media LLC, 2012-08-01)
Let A be a finite nilpotent group acting fixed point freely by automorphisms on the finite solvable group G. It is conjectured that the Fitting length of G is bounded by the number of primes dividing the order of A, counted with multiplicities. The main result of this paper shows that the conjecture is true in the case where A is cyclic of order p (n) q, for prime numbers p and q coprime to 6 and G has abelian Sylow 2-subgroups.
A classification of equivariant principal bundles over nonsingular toric varieties
Biswas, Indranil; Dey, Arijit; Poddar, Mainak (World Scientific Pub Co Pte Lt, 2016-12-01)
We classify holomorphic as well as algebraic torus equivariant principal G-bundles over a nonsingular toric variety X, where G is a complex linear algebraic group. It is shown that any such bundle over an affine, nonsingular toric variety admits a trivialization in equivariant sense. We also obtain some splitting results.
Citation Formats
M. H. Güntürkün, “Using tropical degenerations for proving the nonexistence of certain nets,” Ph.D. - Doctoral Program, Middle East Technical University, 2010.