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Найдено 14 публикаций
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Статья
Panov T., Ustinovskiy Y., Verbitsky M. Mathematische Zeitschrift. 2016. Vol. 284. No. 1. P. 309-333.

Moment-angle manifolds provide a wide class of examples of non-Kähler compact complex manifolds. A complex moment-angle manifold ZZis zero.

 

 

Добавлено: 3 июня 2016
Статья
Feigin E., Finkelberg M. V. Mathematische Zeitschrift. 2013. Vol. 275. No. 1-2. P. 55-77.

Let $Fl^a_\lambda$ be the PBW degeneration of the flag varieties of type $A_{n-1}$. These varieties are singular and are acted upon with the degenerate Lie group $SL_n^a$. We prove that $Fl^a_\lambda$ have rational singularities, are normal and locally complete intersections, and construct a desingularization $R_\lambda$ of $Fl^a_\lambda$. The varieties $R_\lambda$ can be viewed as towers of successive $P^1$-fibrations, thus providing an analogue of the classical Bott-Samelson-Demazure-Hansen desingularization. We prove that the varieties $R_\lambda$ are Frobenius split. This gives us Frobenius splitting for the degenerate flag varieties and allows to prove the Borel-Weil type theorem for $Fl^a_\lambda$. Using the Atiyah-Bott-Lefschetz formula for $R_\la$, we compute the $q$-characters of the highest weight $\msl_n$-modules.

Добавлено: 18 сентября 2013
Статья
Verbitsky M., Vuletescu V., Ornea L. Mathematische Zeitschrift. 2018. P. 1-9.
Добавлено: 9 января 2019
Статья
Cerulli I. G., Fang X., Feigin E. et al. Mathematische Zeitschrift. 2017. Vol. 287. No. 1. P. 615-654.

Linear degenerate flag varieties are degenerations of flag varieties as quiver Grassmannians. For type A flag varieties, we obtain characterizations of flatness, irreducibility and normality of these degenerations via rank tuples. Some of them are shown to be isomorphic to Schubert varieties and can be realized as highest weight orbits of partially degenerate Lie algebras, generalizing the corresponding results on degenerate flag varieties. To study normality, cell decompositions of quiver Grassmannians are constructed in a wider context of equioriented quivers of type A. 

Добавлено: 17 февраля 2017
Статья
Ornea L., Verbitsky M. Mathematische Zeitschrift. 2013. Vol. 273. No. 3-4. P. 605-611.

A manifold M is locally conformally Kähler (LCK) if it admits a Kähler covering M˜ with monodromy acting by holomorphic homotheties. Let M be an LCK manifold admitting a holomorphic conformal flow of diffeomorphisms, lifted to a non-isometric homothetic flow on M˜ . We show that M admits an automorphic potential, and the monodromy group of its conformal weight bundle is Z.

Добавлено: 19 марта 2013
Статья
Ivashkovich S., V. Shevchishin. Mathematische Zeitschrift. 2011. Vol. 268. No. 3-4. P. 1159-1210.

We prove the existence of primitive curves and positivity of intersections of J-complex curves for Lipschitz-continuous almost complex structures. These results are deduced from the Comparison Theorem for J-holomorphic maps in Lipschitz structures, previously known for J of class C1,Lip . We also give the optimal regularity of curves in Lipschitz structures. It occurs to be C1,LnLip , i.e. the first derivatives of a J-complex curve for Lipschitz J are Log-Lipschitz-continuous. A simple example that nothing better can be achieved is given. Further we prove the Genus Formula for J-complex curves and determine their principal Puiseux exponents (all this for Lipschitz-continuous J-s).

Добавлено: 18 марта 2013
Статья
Cheltsov Ivan, Park J., Won J. Mathematische Zeitschrift. 2014. No. 276. P. 51-79.

We study log canonical thresholds on quartic threefolds, quintic fourfolds, and double spaces. As an important application, we show that they have Kähler–Einstein metrics if they are general.

Добавлено: 14 ноября 2013
Статья
Cheltsov I., Ahmadinezhad H. Mathematische Zeitschrift. 2018. Vol. 288. No. 1-2. P. 217-241.

 

 

Добавлено: 13 сентября 2018
Статья
Gorchinskiy Sergey, Viviani F. Mathematische Zeitschrift. 2008. Vol. 258. No. 2. P. 319-331.
Добавлено: 22 февраля 2011
Статья
Verbitsky M. Mathematische Zeitschrift. 2010. Vol. 264. No. 4. P. 939-957.
Добавлено: 12 октября 2012
Статья
Dummigan N., Golyshev V. Mathematische Zeitschrift. 2015.
Добавлено: 23 октября 2017
Статья
Mikhail Skopenkov, Pottmann H., Grohs P. Mathematische Zeitschrift. 2012. Vol. 272. P. 645-674.
Добавлено: 26 сентября 2014
Статья
A. Kuznetsov. Mathematische Zeitschrift. 2014. Vol. 276. No. 3. P. 655-672.
Добавлено: 22 декабря 2013
Статья
Tikhomirov A. S., Bruzzo U., Markushevich D. Mathematische Zeitschrift. 2013. Vol. 275. No. 3-4. P. 1073-1093.
Добавлено: 20 октября 2014