Zobrazeno 1 - 10
of 683
pro vyhledávání: '"14J27"'
In this second part we study first the group $Aut_{\mathbb{Q}}(S)$ of numerically trivial automorphisms of a properly elliptic surface $S$, that is, of a minimal surface with Kodaira dimension $\kappa(S)=1$, in the case $\chi(S) \geq 1$. Our first su
Externí odkaz:
http://arxiv.org/abs/2412.17033
Autor:
Trieu, Thu Ha
We relate the Mahler measure of exact polynomials in arbitrary variables to the Deligne cohomology of the Maillot variety using the Goncharov polylogarithmic complexes. In the four-variable case, we further study the relationship between the Mahler m
Externí odkaz:
http://arxiv.org/abs/2412.00893
We determine explicit generators for the ring of modular forms associated with the moduli spaces of K3 surfaces with automorphism group $(\mathbb{Z}/2\mathbb{Z})^2$ and of Picard rank 13 and higher. The K3 surfaces in question carry a canonical Jacob
Externí odkaz:
http://arxiv.org/abs/2411.05970
Autor:
Martinez, Cristian
We give a proof of the Kodaira vanishing theorem on smooth complex surfaces using geometric stability conditions. Likewise, we give a new proof of a result of Xie characterizing the counterexamples of the Kodaira vanishing theorem in positive charact
Externí odkaz:
http://arxiv.org/abs/2411.03510
We show that K3 surfaces in characteristic 2 can admit sets of $n$ disjoint smooth rational curves whose sum is divisible by 2 in the Picard group, for each $n=8,12,16,20$. More precisely, all values occur on supersingular K3 surfaces, with exception
Externí odkaz:
http://arxiv.org/abs/2410.14085
Autor:
Meira, Felipe Zingali
Let $k$ be a number field and $\mathcal{E}$ an elliptic curve defined over the function field $k(T)$ given by an equation of the form $y^2 = a_3x^3 + a_2x^2 + a_1x + a_0$, where $a_i \in k[T]$ and $deg(a_i) \leq 2$. We explore the conic bundle struct
Externí odkaz:
http://arxiv.org/abs/2410.12066
We study the relative cone conjecture for families of $K$-trivial varieties with vanishing irregularity. As an application we prove that the relative movable and the relative nef cone conjectures hold for fibrations in projective IHS manifolds of the
Externí odkaz:
http://arxiv.org/abs/2410.11987
Autor:
Mendes, Luís Gustavo, Puchuri, Liliana
The blown up complex projective plane in the twelve triple points of the dual Hesse arrangement has an infinite number of irreducible rational curves of self-intersection $-1$, for short, $(-1)$-curves. In the preprint version of [Dumnicki, 2019], T.
Externí odkaz:
http://arxiv.org/abs/2409.19235
Autor:
Greer, François, Zhang, Yilong
We construct a family of elliptic surfaces with $p_g=q=1$ that arise from base change of the Hesse pencil. We identify explicitly a component of the higher Noether-Lefschetz locus with positive Mordell-Weil rank, and a particular surface having maxim
Externí odkaz:
http://arxiv.org/abs/2409.18927
We study the embedded topology of certain conic-line arrangements of degree 7. Two new examples of Zariski pairs are given. Furthermore, we determine the number of connected components of the conic-line arrangements. We also calculate the fundamental
Externí odkaz:
http://arxiv.org/abs/2409.05011