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Regular version of the site
Of all publications in the section: 7
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Article
Sergeev A. Michigan Mathematical Journal. 2001. No. 49. P. 113-146.
Added: Sep 8, 2014
Article
Lvovsky S. Michigan Mathematical Journal. 1992. Vol. 39. P. 41-51.
Added: Jun 11, 2010
Article
Lvovsky S. Michigan Mathematical Journal. 1992. Vol. 39. P. 65-70.
Added: Jun 11, 2010
Article
Basalaev A., Priddis N. Michigan Mathematical Journal. 2018. Vol. 67. No. 2. P. 333-369.

In this paper we consider the orbifold curve, which is a quotient of an elliptic curve $\mathcal{E}$ by a cyclic group of order 4. We develop a systematic way to obtain a Givental-type reconstruction of Gromov-Witten theory of the orbifold curve via the product of the Gromov-Witten theories of a point. This is done by employing mirror symmetry and certain results in FJRW theory. In particular, we present the particular Givental's action giving the CY/LG correspondence between the Gromov-Witten theory of the orbifold curve $\mathcal{E} / \mathbb{Z}_4$ and FJRW theory of the pair defined by the polynomial $x^4+y^4+z^2$ and the maximal group of diagonal symmetries. The methods we have developed can easily be applied to other finite quotients of an elliptic curve. Using Givental's action we also recover this FJRW theory via the product of the Gromov-Witten theories of a point. Combined with the CY/LG action we get a result in "pure" Gromov-Witten theory with the help of modern mirror symmetry conjectures.

Added: Feb 26, 2019
Article
Altmann K., Kiritchenko V., Petersen L. Michigan Mathematical Journal. 2015. Vol. 64. P. 3-38.

Given a spherical homogeneous space G/H of minimal rank, we provide a simple procedure to describe its embeddings as varieties with torus action in terms of divisorial fans. The torus in question is obtained as the identity component of the quotient group N/H, where N is the normalizer of H in G. The resulting Chow quotient is equal to (a blowup of) the simple toroidal compactification of G/(H N^0). In the horospherical case, for example, it is equal to a flag variety, and the slices (coefficients) of the divisorial fan are merely shifts of the colored fan along the colors.

Added: Apr 3, 2015
Article
Prokhorov Y. Michigan Mathematical Journal. 2015. Vol. 64. No. 2. P. 293-318.

We prove that, except for a few cases, stable linearizability of finite subgroups of the plane Cremona group implies linearizability. © 2015, University of Michigan. All rights reserved.

Added: Sep 8, 2015
Article
Arzhantsev I., Liendo A. Michigan Mathematical Journal. 2012. Vol. 61. No. 4. P. 731-762.

In this paper we classify SL_2-actions on normal affine T-varieties that are normalized by the torus T. This is done in terms of a combinatorial description of T-varieties given by Altmann and Hausen. The main ingredient is a generalization of Demazure's roots of the fan of a toric variety. As an application we give a description of special SL_2-actions on normal affine varieties. We also obtain, in our terms, the classification of quasihomogeneous SL_2-threefolds due to Popov.

Added: Feb 5, 2013