arXiv subjects

Sadık Terzi

Publications and source records attributed to Sadık Terzi.

3 recordsLinked to original sources

arXiv2024

On the p-rank of singular curves and their smooth models

In this paper, we are concerned with the computation of the $p$-rank and $a$-number of singular curves and their smooth model. We consider a pair $X, X'$ of proper curves over an algebraically closed field $k$ of characteristic $p$, where $X'$ is a singular curve which lies on a smooth projective variety, particularly on smooth projective surfaces $S$ (with $p_g(S) = 0 = q(S)$) and $X$ is the smooth model of $X'$. We determine the $p$-rank of $X$ by using the exact sequence of group schemes relating the Jacobians $J_X$ and $J_{X'}$. As an application, we determine a relation about the fundamental invariants $p$-rank and $a$-number of a family of singular curves and their smooth models. Moreover, we calculate $a$-number and find lower bound for $p$-rank of a family of smooth curves.

math.AG↗

arXiv2024

On the p-rank of curves

In this paper, we are concerned with the computations of the $p$-rank of curves in two different setups. We first work with complete intersection varieties in $\mb{P}^n \text{ for}~n\ge 2$ and compute explicitly the action of Frobenius on the top cohomology group. In case of curves and surfaces, this information suffices to determine if the variety is ordinary. Next, we consider curves on more general surfaces with $p_g(S) = 0 = q(S)$ such as Hirzebruch surfaces and determine $p$-rank of curves on Hirzebruch surfaces.

math.AG↗

arXiv2021

On the BMY inequality on surfaces

In this paper, we are concerned with the relation between the ordinarity of surfaces of general type and the failure of the BMY inequality in positive characteristic. We consider semistable fibrations $π:S \longrightarrow C$ where $S$ is a smooth projective surface and $C$ is a smooth projective curve. Using the exact sequence relating the locally exact differential forms on $S$, $C$, and $S/C$, we prove an inequality relating $c_1^2$ and $c_2$ for ordinary surfaces which admit generically ordinary semistable fibrations. This inequality differs from the BMY inequality by a correcting term which vanishes if the fibration is ordinary.

math.AG↗