ﻻ يوجد ملخص باللغة العربية
We consider a family of surfaces of general type $S$ with $K_S$ ample, having $K^2_S = 24, p_g (S) = 6, q(S)=0$. We prove that for these surfaces the canonical system is base point free and yields an embedding $Phi_1 : S rightarrow mathbb{P}^5$. This result answers a question posed by G. and M. Kapustka. We discuss some related open problems, concerning also the case $p_g(S) = 5$, where one requires the canonical map to be birational onto its image.
We give new contributions to the existence problem of canonical surfaces of high degree. We construct several families (indeed, connected components of the moduli space) of surfaces $S$ of general type with $p_g=5,6$ whose canonical map has image $Si
A theta surface in affine 3-space is the zero set of a Riemann theta function in genus 3. This includes surfaces arising from special plane quartics that are singular or reducible. Lie and Poincare showed that theta surfaces are precisely the surface
In this paper, we classified the surfaces whose canonical maps are abelian covers over $mathbb{P}^2$. Moveover, we construct a new Campedelli surface with fundamental group $mathbb{Z}_2^{oplus 3}$ and give defining equations for Persssons surface and
The Quillen connection on ${mathcal L} rightarrow {mathcal M}_g$, where ${mathcal L}^*$ is the Hodge line bundle over the moduli stack of smooth complex projective curves curves ${mathcal M}_g$, $g geq 5$, is uniquely determined by the condition that
We prove the unirationality of the Ueno-type manifold $X_{4,6}$. $X_{4,6}$ is the minimal resolution of the quotient of the Cartesian product $E(6)^4$, where $E(6)$ is the equianharmonic elliptic curve, by the diagonal action of a cyclic group of ord