Products of pairs of Dehn twists and maximal real Lefschetz fibrations

We address the problem of existence and uniqueness of a factorization of a given element of the modular group into a product of two Dehn twists. As a geometric application, we conclude that any maximal real elliptic Lefschetz fibration is algebraic.Comment: Final version accepted for publicatio

Products of pairs of Dehn twists and maximal real Lefschetz fibrations

We address the problem of existence and uniqueness of a factorization of a given element of the modular group into a product of two Dehn twists. As a geometric application, we conclude that any maximal real elliptic Lefschetz bration is algebraic

Laguerre near-planes of order four

We investigate Laguerre near-planes of order 4 and classify all such planes. We further develop various descriptions of these planes and characterise those Laguerre near-planes that can be extended to the Miquelian Laguerre plane. We also determine the automorphism groups of these planes and give characterisations of some of the planes in terms of their automorphism groups

Moduli of real pointed quartic curves

We describe a natural open stratum in the moduli space of smooth real pointed quartic curves in the projective plane. This stratum consists of real isomorphism classes of pairs $(C, p)$ with $p$ a real point on the curve $C$ such that the tangent line at $p$ intersects the curve in two distinct points besides $p$. We will prove that this stratum consists of $20$ connected components. Each of these components has a real toric structure defined by an involution in the Weyl group of type $E_7$

Hyperplanes of symplectic dual polar spaces : a survey

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