François Greer

activity

20172020

collaborators

4 papers

math.AG2020

Nodal elliptic curves on K3 surfaces

Nathan Chen, François Greer, Ruijie Yang

Let $(X, L)$ be a general primitively polarized K3 surface with $c_{1} (L)^{2} = 2 g - 2$ for some integer $g \geq 2$ . The Severi variety $V^{L, δ} \subset ∣ L ∣$ is defined to be the locus of…

math.SG2018

A Lagrangian sphere which is not a vanishing cycle

François Greer

We give examples of Calabi-Yau threefolds containing Lagrangian spheres which are not vanishing cycles of nodal degenerations, answering a question of Donaldson in the negative.

math.AG2018

Modular forms from Noether-Lefschetz theory

François Greer

We enumerate smooth rational curves on very general Weierstrass fibrations over hypersurfaces in projective space. The generating functions for these numbers lie in the ring of cla…

math.AG2017

Counting Curves on a Weierstrass Model

Francois Greer

Let $X \to P^{2}$ be the elliptic Calabi-Yau threefold given by a general Weierstrass equation. We answer the enumerative question of how many discrete rational curves lie ove…