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pro vyhledávání: '"Viray, Bianca"'
Autor:
Creutz, Brendan, Viray, Bianca
Previous work of the authors showed that every quartic del Pezzo surface over a number field has index dividing $2$, and asked whether such surfaces always have a closed point of degree $2$. We resolve this by constructing infinitely many quartic del
Externí odkaz:
http://arxiv.org/abs/2408.08436
Autor:
Viray, Bianca, Vogt, Isabel
We give a self-contained introduction to isolated points on curves and their counterpoint, parameterized points, that situates these concepts within the study of the arithmetic of curves. In particular, we show how natural geometric constructions of
Externí odkaz:
http://arxiv.org/abs/2406.14353
A double cover $Y$ of $\mathbb{P}^1 \times \mathbb{P}^2$ ramified over a general $(2,2)$-divisor will have the structure of a geometrically standard conic bundle ramified over a smooth plane quartic $\Delta \subset \mathbb{P}^2$ via the second projec
Externí odkaz:
http://arxiv.org/abs/2406.13510
Autor:
Berg, Jennifer, Pagano, Carlo, Poonen, Bjorn, Stoll, Michael, Triantafillou, Nicholas, Viray, Bianca, Vogt, Isabel
On a projective variety defined over a global field, any Brauer--Manin obstruction to the existence of rational points is captured by a finite subgroup of the Brauer group. We show that this subgroup can require arbitrarily many generators.
Comm
Comm
Externí odkaz:
http://arxiv.org/abs/2309.05931
Autor:
Creutz, Brendan, Viray, Bianca
Let $W/K$ be a nonempty scheme over the field of fractions of a Henselian local ring $R$. A result of Gabber, Liu and Lorenzini shows that the GCD of the set of degrees of closed points on $W$ (which is called the index of $W/K$) can be computed from
Externí odkaz:
http://arxiv.org/abs/2306.01267
Autor:
Viray, Bianca
These lecture notes give an introduction to the Brauer-Manin obstruction to the existence of rational points, focusing on the interplay between theory and computation.
Comment: 19 pages
Comment: 19 pages
Externí odkaz:
http://arxiv.org/abs/2303.17796
Publikováno v:
Algebr. Geom. 11 (3) (2024) 421-459
We undertake a study of conic bundle threefolds $\pi\colon X\to W$ over geometrically rational surfaces whose associated discriminant covers $\tilde{\Delta}\to\Delta\subset W$ are smooth and geometrically irreducible. First, we determine the structur
Externí odkaz:
http://arxiv.org/abs/2207.07093
Autor:
Rivera, Carlos, Viray, Bianca
Let $X$ be a cubic surface over a global field $k$. We prove that a Brauer-Manin obstruction to the existence of $k$-points on $X$ will persist over every extension $L/k$ with degree relatively prime to $3$. In other words, a cubic surface has nonemp
Externí odkaz:
http://arxiv.org/abs/2111.03546
Autor:
Creutz, Brendan, Viray, Bianca
Publikováno v:
Alg. Number Th. 17 (2023) 1411-1452
We prove that a smooth complete intersection of two quadrics of dimension at least $2$ over a number field has index dividing $2$, i.e., that it possesses a rational $0$-cycle of degree $2$.
Comment: 39 pages. Section on local fields moved to S2
Comment: 39 pages. Section on local fields moved to S2
Externí odkaz:
http://arxiv.org/abs/2106.08560
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