Abstracts for Seminar Algebraic Geometry (SAG)

Gromov-Witten invariants counts the number of pseudo-holomorphic curves. One often write them in terms of generating functions. Occasionally, it posses some very beautiful properties such as being a quasi-modular form. In the talk, we will explain this phenomenon for elliptic orbifold P1. This is a joint work with Milanov, Krawitz and Shen.

We present a strategy for proving that full exceptional collections of vector bundles on projective n-space can be constructed from a standard collection of line bundles, reducing the question of constructibility to the problem of freeness of a certain finitely generated linear group. We use the ping-pong lemma of Fricke-Klein to solve this problem in low dimensions, thus providing a new proof of constructibility of exceptional collections in some cases.

We analyze the GIT-quotient of the symplectic grassmannian parametrizing lagrangian subspaces of $\bigwedge3{\mathbb C}6$ modulo PGL(6) - a compactification of the moduli space of double EPW-sextics. The family of double EPW-sextics is similar to the family of cubic 4-folds. Our final goal will be to analyze the period map from the GIT-quotient to the Baily-Borel compactification of the relevant bounded symmetric domain. We are inspired by the works of C.Voisin, B. Hassett, R.Laza and E. Looijenga on periods of cubic 4-folds.