ترغب بنشر مسار تعليمي؟ اضغط هنا

Higher-dimensional Calabi-Yau varieties with dense sets of rational points

84   0   0.0 ( 0 )
 نشر من قبل Fumiaki Suzuki
 تاريخ النشر 2021
  مجال البحث
والبحث باللغة English
 تأليف Fumiaki Suzuki




اسأل ChatGPT حول البحث

We construct higher-dimensional Calabi-Yau varieties defined over a given number field with Zariski dense sets of rational points. We give two elementary constructions in arbitrary dimensions as well as another construction in dimension three which involves certain Calabi-Yau threefolds containing an Enriques surface. The constructions also show that potential density holds for (sufficiently) general members of the families.

قيم البحث

اقرأ أيضاً

192 - Jinsong Xu 2016
We prove a structure theorem for the Albanese maps of varieties with Q-linearly trivial log canonical divisors. Our start point is the action of a nonlinear algebraic group on a projective variety.
We construct a global B-model for weighted homogeneous polynomials based on K. Saitos theory of primitive forms. Our main motivation is to give a rigorous statement of the so called global mirror symmetry conjecture relating Gromov-Witten invariants and Fan--Jarvis--Ruan--Witten invariants. Furthermore, our construction allows us to generalize the notion of a quasi-modular form and holomorphic anomaly equations. Finally, we prove the global mirror symmetry conjecture for the Fermat polynomials.
We give a criterion for a nef divisor $D$ to be semiample on a Calabi--Yau threefold $X$ when $D^3=0=c_2(X)cdot D$ and $c_3(X) eq 0$. As a direct consequence, we show that on such a variety $X$, if $D$ is strictly nef and $ u(D) eq 1$, then $D$ is am ple; we also show that if there exists a nef non-ample divisor $D$ with $D otequiv 0$, then $X$ contains a rational curve when its topological Euler characteristic is not $0$.
Let $C$ be a hyperelliptic curve of genus $g$ over the fraction field $K$ of a discrete valuation ring $R$. Assume that the residue field $k$ of $R$ is perfect and that $mathop{textrm{char}} k eq 2$. Assume that the Weierstrass points of $C$ are $K$ -rational. Let $S = mathop{textrm{Spec}} R$. Let $mathcal{X}$ be the minimal proper regular model of $C$ over $S$. Let $mathop{textrm{Art}} (mathcal{X}/S)$ denote the Artin conductor of the $S$-scheme $mathcal{X}$ and let $ u (Delta)$ denote the minimal discriminant of $C$. We prove that $-mathop{textrm{Art}} (mathcal{X}/S) leq u (Delta)$. As a corollary, we obtain that the number of components of the special fiber of $mathcal{X}$ is bounded above by $ u(Delta)+1$.
134 - Duco van Straten 2017
Motivated by mirror symmetry of one-parameter models, an interesting class of Fuchsian differential operators can be singled out, the so-called Calabi--Yau operators, introduced by Almkvist and Zudilin. They conjecturally determine $Sp(4)$-local syst ems that underly a $mathbb{Q}$-VHS with Hodge numbers [h^{3 0}=h^{2 1}=h^{1 2}=h^{0 3}=1] and in the best cases they make their appearance as Picard--Fuchs operators of families of Calabi--Yau threefolds with $h^{12}=1$ and encode the numbers of rational curves on a mirror manifold with $h^{11}=1$. We review some of the striking properties of this rich class of operators.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا