3,133 research outputs found
On automorphism groups of affine surfaces
This is a survey on the automorphism groups in various classes of affine
algebraic surfaces and the algebraic group actions on such surfaces. Being
infinite-dimensional, these automorphism groups share some important features
of algebraic groups. At the same time, they can be studied from the viewpoint
of the combinatorial group theory, so we put a special accent on
group-theoretical aspects (ind-groups, amalgams, etc.). We provide different
approaches to classification, prove certain new results, and attract attention
to several open problems.Comment: Proposition 2.10 from the previous version (published in Algebraic
Varieties and Automorphism Groups, ASPM 75) deleted. There is a mistake in
the proof kindly indicated by J.-P. Furter; the validity of the result
remains open. This does not affect the rest of the pape
An alternative description of the Drinfeld p-adic half-plane
We show that the Deligne formal model of the Drinfeld p-adic halfplane
relative to a non-archimedean local field F represents a moduli problem of
polarized O_F-modules with an action of the ring of integers O_E in a quadratic
extension E of F. The proof proceeds by establishing a comparison isomorphism
with the Drinfeld moduli problem. This isomorphism reflects the accidental
isomorphism of SL_2(F) and SU(C)(F) for a two-dimensional split hermitian space
C for E/F.Comment: 18pp, Concluding remarks section revised. Typos correcte
Lecture Notes on Noncommutative Algebraic Geometry and Noncommutative Tori
The first part of these notes gives an introduction to noncommutative
projective geometry after Artin--Zhang. The second part provides an overview of
the work of Polishchuk that reconciles noncommutative two-tori having real
multiplication with the Artin--Zhang setting.Comment: Final version - exposition improved; a proof of the derived
equivalence added (Prop. 3.8). To appear in the proceedings volume of the
"International Workshop on Noncommutative Geometry", IPM, Tehran 200
Donaldson-Thomas invariants and wall-crossing formulas
Notes from the report at the Fields institute in Toronto. We introduce the
Donaldson-Thomas invariants and describe the wall-crossing formulas for
numerical Donaldson-Thomas invariants.Comment: 18 pages. To appear in the Fields Institute Monograph Serie
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