Description of the Connected Components of a Semialgebraic Set in Single Exponential Time.
The moduli space of stable vector bundles over a moving curve is constructed, and on this a generalized Weil-Petersson form is constructed. Using the local Riemann-Roch formula of Bismut-Gillet-Soulé it is shown that the generalized Weil-Petersson form is the curvature of the determinant line bundle, equipped with the Quillen metric, for a vector bundle on the fiber product of the universal moduli space with the universal curve.
We prove that the bounded derived category of the surface constructed by Barlow admits a length 11 exceptional sequence consisting of (explicit) line bundles. Moreover, we show that in a small neighbourhood of in the moduli space of determinantal Barlow surfaces, the generic surface has a semiorthogonal decomposition of its derived category into a length 11 exceptional sequence of line bundles and a category with trivial Grothendieck group and Hochschild homology, called a phantom category....
Nous étudions deux nouvelles composantes irréductibles du bord de la variété des instantons de degré 3. Nous décrivons grâce aux transformations cubo-cubiques involutives déduites de la monade de Beilinson (ce sont des transformations de Cremona particulières). Nous exhibons alors les deux composantes du bord par dégénérescence sur les transformations. Nous mettons en évidence la dualité qui les lie : les transformations cubo-cubiques de l’une sont les inverses de l’autre. Nous décrivons en...