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The Manin-Peyre conjecture is established for smooth spherical Fano threefolds of semisimple rank one and type N. Together with the previously solved case T and the toric cases, this covers all types of smooth spherical Fano threefolds. The case N fe
Externí odkaz:
http://arxiv.org/abs/2203.14841
The Manin-Peyre conjecture is established for a class of smooth spherical Fano varieties of semisimple rank one. This includes all smooth spherical Fano threefolds of type T as well as some higher-dimensional smooth spherical Fano varieties.
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Externí odkaz:
http://arxiv.org/abs/2004.09357
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Autor:
Borovoi, Mikhail, Gagliardi, Giuliano
Let $k_0$ be a field of characteristic $0$ with algebraic closure $k$. Let $G$ be a connected reductive $k$-group, and let $Y$ be a spherical variety over $k$ (a spherical homogeneous space or a spherical embedding). Let $G_0$ be a $k_0$-model ($k_0$
Externí odkaz:
http://arxiv.org/abs/1810.08960
Autor:
Borovoi, Mikhail, Gagliardi, Giuliano
Publikováno v:
Transform. Groups 25 (2020), 391-439
Let $G$ be a connected semisimple group over an algebraically closed field $k$ of characteristic 0. Let $Y=G/H$ be a spherical homogeneous space of $G$, and let $Y'$ be a spherical embedding of $Y$. Let $k_0$ be a subfield of $k$. Let $G_0$ be a $k_0
Externí odkaz:
http://arxiv.org/abs/1710.02471
Autor:
Derenthal, Ulrich, Gagliardi, Giuliano
Publikováno v:
Adv. Math. 337 (2018), 39-82
We prove Manin's conjecture on the asymptotic behavior of the number of rational points of bounded anticanonical height for a spherical threefold with canonical singularities and two infinite families of spherical threefolds with log terminal singula
Externí odkaz:
http://arxiv.org/abs/1611.04754
Autor:
Batyrev, Victor, Gagliardi, Giuliano
Publikováno v:
Proc. Amer. Math. Soc. 146 (2018), no. 1, 29-41
We are interested in stringy invariants of singular projective algebraic varieties satisfying a strict monotonicity with respect to elementary birational modifications in the Mori program. We conjecture that the algebraic stringy Euler number is one
Externí odkaz:
http://arxiv.org/abs/1610.03842
Autor:
Gagliardi, Giuliano
Given the Luna-Vust invariants of a spherical variety, we determine the Luna-Vust invariants of the spectrum of its Cox ring. In particular, we deduce an explicit description of the divisor class group of the Cox ring. It follows that every spherical
Externí odkaz:
http://arxiv.org/abs/1608.08151
Publikováno v:
Trans. Amer. Math. Soc. 369 (2017), 2615-2649
We associate to any complete spherical variety $X$ a certain nonnegative rational number $\wp(X)$, which we conjecture to satisfy the inequality $\wp(X) \le \operatorname{dim} X - \operatorname{rank} X$ with equality holding if and only if $X$ is iso
Externí odkaz:
http://arxiv.org/abs/1412.6084
Akademický článek
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