Zobrazeno 1 - 10
of 710
pro vyhledávání: '"14Q10"'
Autor:
Logan, Adam
The modularity of an elliptic curve $E/\mathbb Q$ can be expressed either as an analytic statement that the $L$-function is the Mellin transform of a modular form, or as a geometric statement that $E$ is a quotient of a modular curve $X_0(N)$. For el
Externí odkaz:
http://arxiv.org/abs/2411.08269
In this paper we use algebraic curves and other algebraic number theory methods to show the validity of a permutation polynomial conjecture regarding $f(X)=X^{q(p-1)+1} +\alpha X^{pq}+X^{q+p-1}$, on finite fields $\mathbb{F}_{q^2}, q=p^k$, from [A. R
Externí odkaz:
http://arxiv.org/abs/2410.22692
We introduce surfaces at infinity, a class of rational surfaces linked to curves with only one place at infinity. The cone of curves of these surfaces is finite polyhedral and minimally generated. We also introduce the $\delta$-semigroup of a surface
Externí odkaz:
http://arxiv.org/abs/2408.15931
Autor:
Pichon-Pharabod, Eric
We provide an algorithm for computing an effective basis of homology of elliptic surfaces over the complex projective line on which integration of periods can be carried out. This allows the heuristic recovery of several algebraic invariants of the s
Externí odkaz:
http://arxiv.org/abs/2401.05131
Autor:
Qureshi, Muhammad Imran
We construct two types of wellformed and quasismooth biregular models (infinite series) of rigid orbifold del Pezzo surfaces having their (sub) anti-canonical embeddings in $\mathbb P^6(w_i) $. One type of model contains a family of rigid del Pezzo s
Externí odkaz:
http://arxiv.org/abs/2312.17339
Autor:
Brandhorst, Simon, Zach, Matthias
We explain how to use the computer algebra system OSCAR to find all elliptic fibrations (up to automorphism) on a given surface and compute their Weierstrass models. This is illustrated for Vinberg's most algebraic K3 surface, the unique K3 surface o
Externí odkaz:
http://arxiv.org/abs/2311.11766
Autor:
Logan, Adam, Patashnick, Owen
For the family of Kummer surfaces of the square of an elliptic curve over the prime field $\mathbb{F}_p$ with $p$ odd, we show that if the automorphism group acts transitively on the set of points then the action is at least alternating. This is anal
Externí odkaz:
http://arxiv.org/abs/2311.04353
Brandhorst and Shimada described a large class of Enriques surfaces, called $(\tau,\overline{\tau})$-generic, for which they gave generators for the automorphism groups and calculated the elliptic fibrations and the smooth rational curves up to autom
Externí odkaz:
http://arxiv.org/abs/2309.14981
We find explicit equations of the fake projective plane $(a=7,p=2,\emptyset,D_3 X_7)$, which lies in the same class as the fake projective plane $(a=7,p=2,\emptyset,D_3 2_7)$ with $21$ automorphisms whose equations were previously found by Borisov an
Externí odkaz:
http://arxiv.org/abs/2308.14237
A fake projective plane is a complex surface with the same Betti numbers as $\mathbb{C} P^2$ but not biholomorphic to it. We study the fake projective plane $\mathbb{P}_{\operatorname{fake}}^2 = (a = 7, p = 2, \emptyset, D_3 2_7)$ in the Cartwright-S
Externí odkaz:
http://arxiv.org/abs/2308.10429