Advanced Algebra and Geometry

The differential calculus on the quantum supergroup was introduced by Schmidke et al (1990 Z. Phys. C 48 249). We construct a differential calculus on the quantum supergroup in a different way and obtain its quantum Lie algebra. The main structures are derived without an R -matrix. It is shown that the results can be…

Abstract We introduce a family of algebraic curves over 𝔽 q 2n (for an odd n) and show that they are maximal. When n = 3, our curve coincides with the 𝔽 q 6 -maximal curve that has been found by Giulietti and Korchmáros recently. Their curve (i.e., the case n = 3) is the first example of a maximal curve proven not to…

We study complex plane projective sextic curves with simple singularities up to equisingular deformations. It is shown that two such curves are deformation equivalent if and only if the corresponding pairs are diffeomorphic. A way to enumerate all deformation classes is outlined, and a few examples are considered, inc…

We consider the model theory of the real and complex fields with a multiplicative group having the Mann property. Among these groups are the finitely generated multiplicative groups in these fields. As a by-product we obtain some results on groups with the Mann property in rings of Witt vectors and in fields of positi…

• AYHAN GÜNAYDIN

No abstract yet.

The main result of this paper is that any compact Stein surface with boundary embeds naturally into a symplectic Lefschetz fibration over S2. Also along the way we obtain the following results. (1) There exists a minimal elliptic fibration over D2, which is not Stein. (2) The circle bundle over a genus n ≥ 2 surface w…

Let M be a smooth 4-manifold which admits a Lefschetz fibration over D 2 or S 2 .We develop an algorithm to compute the signature of M using the global monodromy of this fibration.As a corollary we prove that there is no hyperelliptic Lefschetz fibration over S 2 with only reducible singular fibers.

No abstract yet.

• ZÜBEYİR ÇINKIR

There exists a (relatively minimal) genus g g Lefschetz fibration with only one singular fiber over a closed (Riemann) surface of genus h h iff g ≥ 3 g \geq 3 and h ≥ 2 h \geq 2 . The singular fiber can be chosen to be reducible or irreducible. Other results are that every Dehn twist on a closed surface of genus at le…

There exists a (relatively minimal) genus g g Lefschetz fibration with only one singular fiber over a closed (Riemann) surface of genus h h iff g ≥ 3 g \geq 3 and h ≥ 2 h \geq 2 . The singular fiber can be chosen to be reducible or irreducible. Other results are that every Dehn twist on a closed surface of genus at le…

• MUSTAFA KORKMAZ

No abstract yet.

No abstract yet.

• ERDOĞAN ŞEN