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The moduli space of stable supercurves and its canonical line bundle
Giovanni Felder, David Kazhdan, Alexander Polishchuk
We prove that the moduli of stable supercurves with punctures is a smooth proper DM stack and study an analog of the Mumford's isomorphism for its canonical line bundle.
Regularity of the superstring supermeasure and the superperiod map
Giovanni Felder, David Kazhdan, Alexander Polishchuk
The supermeasure whose integral is the genus vacuum amplitude of superstring theory is potentially singular on the locus in the moduli space of supercurves where the correspond…
The classical master equation
Giovanni Felder, David Kazhdan
We formalize the construction by Batalin and Vilkovisky of a solution of the classical master equation associated with a regular function on a nonsingular affine variety (the class…
Gaudin subalgebras and stable rational curves
Leonardo Aguirre, Giovanni Felder, Alexander P. Veselov
Gaudin subalgebras are abelian Lie subalgebras of maximal dimension spanned by generators of the Kohno-Drinfeld Lie algebra t_n. We show that Gaudin subalgebras form a variety isom…
Differential operators on toric varieties and Fourier transform
Giovanni Felder, Carlo A. Rossi
We show that Fourier transforms on the Weyl algebras have a geometric counterpart in the framework of toric varieties, namely they induce isomorphisms between twisted rings of diff…