Troisi\`eme groupe de cohomologie non ramifi\'ee des torseurs universels sur les surfaces rationnelles [PDF]
Épijournal de Géométrie Algébrique, 2018 Let $k$ a field of characteristic zero. Let $X$ be a smooth, projective, geometrically rational $k$-surface. Let $\mathcal{T}$ be a universal torsor over $X$ with a $k$-point et $\mathcal{T}^c$ a smooth compactification of $\mathcal{T}$. There is an open
Yang Cao
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Software Engineering and Complexity in Effective Algebraic Geometry [PDF]
, 2012 We introduce the notion of a robust parameterized arithmetic circuit for the evaluation of algebraic families of multivariate polynomials. Based on this notion, we present a computation model, adapted to Scientific Computing, which captures all known ...
Heintz, Joos +2 more
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Troisi\`eme groupe de cohomologie non ramifi\'ee d'un solide cubique sur un corps de fonctions d'une variable [PDF]
Épijournal de Géométrie Algébrique, 2018 En combinant une m\'ethode de C. Voisin avec la descente galoisienne sur le groupe de Chow en codimension $2$, nous montrons que le troisi\`eme groupe de cohomologie non ramifi\'ee d'un solide cubique lisse d\'efini sur le corps des fonctions d'une ...
Jean-Louis Colliot-Thélène +1 more
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Hyperelliptic classes are rigid and extremal in genus two [PDF]
Épijournal de Géométrie Algébrique, 2020 We show that the class of the locus of hyperelliptic curves with $\ell$ marked Weierstrass points, $m$ marked conjugate pairs of points, and $n$ free marked points is rigid and extremal in the cone of effective codimension-($\ell + m$) classes on ...
Vance Blankers
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Gromov–Hausdorff limits of Kähler manifolds and algebraic geometry, II [PDF]
, 2015 In this paper we continue to study Gromov-Hausdorff limits of Kahler manifolds and algebraic geometry. Our main focus is on the algebro-geometric meaning of Riemannian tangent cones and rescaled limits.
S. Donaldson, Song Sun
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Opers of higher types, Quot-schemes and Frobenius instability loci [PDF]
Épijournal de Géométrie Algébrique, 2020 In this paper we continue our study of the Frobenius instability locus in the coarse moduli space of semi-stable vector bundles of rank $r$ and degree $0$ over a smooth projective curve defined over an algebraically closed field of characteristic $p>0 ...
Kirti Joshi, Christian Pauly
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The LLV Algebra for Primitive Symplectic Varieties with Isolated Singularities [PDF]
Épijournal de Géométrie AlgébriqueWe extend results of Looijenga--Lunts and Verbitsky and show that the total Lie algebra $\mathfrak g$ for the intersection cohomology of a primitive symplectic variety $X$ with isolated singularities is isomorphic to $$\mathfrak g \cong \mathfrak{so ...
Benjamin Tighe
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On the irrationality of moduli spaces of projective hyperk\"ahler manifolds [PDF]
Épijournal de Géométrie AlgébriqueThe aim of this paper is to estimate the irrationality of moduli spaces of hyperk\"ahler manifolds of types K3$^{[n]}$, Kum$_{n}$, OG6, and OG10. We prove that the degrees of irrationality of these moduli spaces are bounded from above by a universal
Daniele Agostini +2 more
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Integration-by-parts reductions from unitarity cuts and algebraic geometry [PDF]
, 2015 We show that the integration-by-parts reductions of various two-loop integral topologies can be efficiently obtained by applying unitarity cuts to a specific set of subgraphs and solving associated polynomial (syzygy) equations.
K. J. Larsen, Yang Zhang
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Le probl\`eme de la sch\'ematisation de Grothendieck revisit\'e [PDF]
Épijournal de Géométrie Algébrique, 2020 The objective of this work is to reconsider the schematization problem of [6], with a particular focus on the global case over Z. For this, we prove the conjecture [Conj. 2.3.6][15] which gives a formula for the homotopy groups of the schematization of a
Bertrand Toën
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