Imperial College London
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ProfessorTravisSchedler

Faculty of Natural Sciences, Department of Mathematics

Professor of Mathematics
 
 
 
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Contact

 

t.schedler CV

 
 
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Location

 

622Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Schedler:2017,
author = {Schedler, TJ and Etingof, PI},
journal = {Asian Journal of Mathematics},
pages = {795--868},
title = {Coinvariants of Lie algebras of vector fields on algebraic varieties},
url = {http://hdl.handle.net/10044/1/47879},
volume = {20},
year = {2017}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - We prove that the space of coinvariants of functions on an affine variety by a Lie algebraof vector fields whose flow generates finitely many leaves is finite-dimensional. Cases of the theoreminclude Poisson (or more generally Jacobi) varieties with finitely many symplectic leaves underHamiltonian flow, complete intersections in Calabi-Yau varieties with isolated singularities underthe flow of incompressible vector fields, quotients of Calabi-Yau varieties by finite volume-preservinggroups under the incompressible vector fields, and arbitrary varieties with isolated singularitiesunder the flow of all vector fields. We compute this quotient explicitly in many of these cases. Theproofs involve constructing a natural D-module representing the invariants under the flow of thevector fields, which we prove is holonomic if it has finitely many leaves (and whose holonomicitywe study in more detail). We give many counterexamples to naive generalizations of our results.These examples have been a source of motivation for us.
AU  - Schedler,TJ
AU  - Etingof,PI
EP  - 868
PY  - 2017///
SN  - 1093-6106
SP  - 795
TI  - Coinvariants of Lie algebras of vector fields on algebraic varieties
T2  - Asian Journal of Mathematics
UR  - http://hdl.handle.net/10044/1/47879
VL  - 20
ER  -
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