Journal article
Torsion Type Invariants of Singularities
Vietnam journal of mathematics, Vol.49(2), pp.381-432
06/25/2021
DOI: 10.1007/s10013-021-00510-x
Abstract
Inspired by the LG/CY correspondence, we study the local index theory of the Schrödinger operator associated to a singularity defined on
ℂ
n
by a quasi-homogeneous polynomial
f
. Under some mild assumption to
f
, we show that the small time heat kernel expansion of the corresponding Schrödinger operator exists and is a series of fractional powers of time
t
. Then we prove a local index formula which expresses the Milnor number of
f
by a Gaussian type integration. The heat kernel expansion provides the spectral invariants of
f
. Furthermore, we can define the torsion type invariants associated to a homogeneous singularity. The spectral invariants provide another way to classify the singularity.
Details
- Title: Subtitle
- Torsion Type Invariants of Singularities
- Creators
- Huijun Fan - Peking UniversityHao Fang - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Vietnam journal of mathematics, Vol.49(2), pp.381-432
- Publisher
- Springer Singapore
- DOI
- 10.1007/s10013-021-00510-x
- ISSN
- 2305-221X
- eISSN
- 2305-2228
- Grant note
- 20120001110060 / Doctoral Fund of Ministry of Education of China 100829 / NSF, Division of Mathematical Sciences 11271028; 11325101,11831017,11890660; 11890661 / National Natural Science Foundation of China (https://doi.org/10.13039/501100001809)
- Language
- English
- Date published
- 06/25/2021
- Academic Unit
- Mathematics
- Record Identifier
- 9984240769202771
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