2023/04/27 by Michele Cirafici, Cirafici, Michele
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.2304.14105
openalex publication_date 2023/04/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
K3 surfaces play a prominent role in string theory and algebraic geometry. The properties of their enumerative invariants have important consequences in black hole physics and in number theory. To a K3 surface string theory associates an Elliptic genus, a certain partition function directly related to the theory of Jacobi modular forms. A multiplicative lift of the Elliptic genus produces another modular object, an Igusa cusp form, which is the generating function of BPS invariants of K3 x E. In this note we will discuss a refinement of this chain of ideas. The Elliptic genus can be generalized to the so called Hodge-Elliptic genus which is then related to the counting of refined BPS states of K3 x E. We show how such BPS invariants can be computed explicitly in terms of different versions of the Hodge-Elliptic genus, sometimes in closed form, and discuss some generalizations.