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90 papers · 1 filter
A rationality criterion for real Fano threefolds
Andrea Fanelli, Frédéric Mangolte
We study the connectedness of the real locus of smooth geometrically rational Fano threefolds and prove a sufficient criterion of -rationality.
Płoski Approximation Theorem
Adam Parusiński, Guillaume Rond
The aim of this paper is to review how some approximation results in commutative algebra are being used to construct equisingular deformations of singularities. The first example o…
Equality of tropical rank and dimension for semimodules of tropical rational functions, and computational aspects
Omid Amini, Stéphane Gaubert, Lucas Gierczak
The tropical rank of a semimodule of rational functions on a metric graph mirrors the concept of rank in linear algebra. Defined in terms of the maximal number of tropically indepe…
K-stability of pointless del Pezzo surfaces and Fano 3-folds
Hamid Abban, Ivan Cheltsov, Takashi Kishimoto +1
We explore connections between existence of -rational points for Fano varieties defined over , a subfield of , and existence of Kähler-Einstein metrics on…
On the coefficients of the Zeta-function's L-polynomial for algebraic function fields over finite constant fields
Mahdi Mohamed Koutchoukali
We give an explicit formula of the coefficients of the Zeta-Function's L-polynomial for algebraic function fields over finite constant fields. Thus, we deduce an expression of the…
Quadratic residue patterns, algebraic curves and a K3 surface
Valentina Kiritchenko, Michael Tsfasman, Serge Vladuts +1
Quadratic residue patterns modulo a prime are studied since 19th century. In the first part we extend existing results on the number of consecutive -tuples of quadratic resid…