We consider the problem of computing the Lebesgue volume of compact basic semi-algebraic sets. In full generality, it can be approximated as closely as desired by a converging hierarchy of upper bounds obtained by applying the Moment-SOS (sums of squares) ...
Let (X, Delta) be a projective log canonical Calabi-Yau pair and L an ample Q-line bundle on X, we show that there is a correspondence between lc places of (X, Delta) and weakly special test configurations of (X, Delta; L). ...
Let R be a commutative ring with unit. We endow the categories of filtered complexes and of bicomplexes of R-modules, with cofibrantly generated model structures, where the class of weak equivalences is given by those morphisms inducing a quasi-isomorphism ...
