Counting Higgs bundles
Event details
| Date | 16.10.2014 |
| Hour | 14:15 › 16:00 |
| Speaker | Olivier Schiffmann (Orsay) |
| Location | |
| Category | Conferences - Seminars |
(Note unusual day, time and place of the seminar.)
We give a closed formula (in the form of generating functions) for the number of absolutely
indecomposable vector bundles of given rank and degree on a smooth projective curve X of genus g over a finite field F_q. The answer is given by some polynomial in the Weil numbers of the curve (or, more loosely speaking, in the 'motive' of the
curve). This may be viewed as an analog of the famous theorems of Kac on the number of indecomposable reprsentations of quivers over finite fields.
Adapting ideas of Crawley-Boevey and Van den Bergh, we then show that this number coincides (up to an explicit power of q) with the number of stable Higgs bundles over X (of same rank and degree). This entails a closed formula for the Poincarre
polynomial of the moduli spaces of stable Higgs bundles.
We give a closed formula (in the form of generating functions) for the number of absolutely
indecomposable vector bundles of given rank and degree on a smooth projective curve X of genus g over a finite field F_q. The answer is given by some polynomial in the Weil numbers of the curve (or, more loosely speaking, in the 'motive' of the
curve). This may be viewed as an analog of the famous theorems of Kac on the number of indecomposable reprsentations of quivers over finite fields.
Adapting ideas of Crawley-Boevey and Van den Bergh, we then show that this number coincides (up to an explicit power of q) with the number of stable Higgs bundles over X (of same rank and degree). This entails a closed formula for the Poincarre
polynomial of the moduli spaces of stable Higgs bundles.
Practical information
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