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Oct
23
Moduli spaces of 1-dimensional sheaves play an important role in the enumerative geometry of Calabi-Yau threefolds. In particular, the perverse filtration on their cohomology, induced by a natural support map, encodes the so-called BPS invariants which are expected to be “χ-independent”, where χ…
Oct
23
Oct
26
Jacobi's theta function $\Theta(q) := 1 + 2q + 2q^4 + 2q^9 + \cdots $, and more generally the theta functions associated to positive-definite quadratic forms, have the property that they are modular forms of half-integral weight. The usual proof of this fact is completely analytic in nature,…
Oct
27
Oct
28