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Алгебраическая геометрия и ее приложения

2018
Руководитель: Каледин Дмитрий Борисович, Богомолов Федор Алексеевич
Подразделение: Лаборатория алгебраической геометрии и ее приложений

Цель исследования: получение новых результатов в области алгебраической и дифференциальной геометрии. 

Задачи исследования: 

  • получение новых результатов о производных категориях алгебраических многообразий и их применение к классическим вопросам алгебраической геометрии;
  • развитие методов некоммутативной геометрии;
  • получение новых результатов о специальных многообразиях;
  • изучение геометрии многообразий Фано и других классических вопросов алгебраической геометрии, включая бирациональные вопросы;- получение новых результатов в геометрической теории представлений.

Публикации по проекту:


Braverman A., Michael F. Twisted zastava and q-Whittacker functions // Journal of the London Mathematical Society. 2017. Vol. 96. No. 2. P. 309-325. doi
Prokhorov Y., Mori S. Threefold extremal curve germs with one non-Gorenstein point / Cornell University. Series math "arxiv.org". 2018. 
Verbitsky M., Mj Mahan, Biswas I. Stable Higgs bundles over positive principal elliptic fibrations / Cornell University. Series arxive "math". 2018. 
Ostrik V. Remarks on global dimensions of fusion categories / Cornell University. Series arxive "math". 2018. 
Bogomolov F. A., Blum-Smith B. Purely noncommuting groups / Cornell University. Series arxive "math". 2018. 
Румынин Д. А., Kirkina K., Capdeboscq I. Presentation of affine Kac-Moody groups // Forum of Mathematics, Sigma. 2018. Vol. 6. P. 1-35. doi
Kuznetsov A., Prokhorov Y. Prime Fano threefolds of genus 12 with a Gm-action and their automorphisms // Épijournal de Géométrie Algébrique. 2018. Vol. 2. No. 3. P. 1-14. 
Trepalin A. Quotients of del Pezzo Surfaces of Degree 2 // Moscow Mathematical Journal. 2018. Vol. 18. No. 3. P. 557-597. 
Shoikhet B. On the twisted tensor product of small dg categories / Cornell University. Series arxive "math". 2018. 
Guseva L. On the derived category of IGr(3,8) / Cornell University. Series math "arxiv.org". 2018. 
Ostrik V., Etingof P. On semisimplification of tensor categories / Cornell University. Series arxive "math". 2018. 
Kuznetsov A., Smirnov M. On residual categories for Grassmannians / Cornell University. Series arxive "math". 2018. 
Loginov K. On non-rational fibers of del Pezzo fibrations over curves / Cornell University. Series arxive "math". 2018. 
Shramov K., Ciliberto C., Farnik M., Küronya A., Lozovanu V., Roé Joaquim Newton-Okounkov bodies sprouting on the valuative tree // Rendiconti del Circolo Matematico di Palermo. 2017. Vol. 66. No. 2. P. 161-194. doi
Shoikhet B. On a higher structure on operadic deformation complexes // Theory and Applications of Categories. 2018. Vol. 33. No. 32. P. 988-1030. 
Polishchuk A., Hua Zheng Shifted Poisson structures and moduli spaces of complexes // Advances in Mathematics. 2018. Vol. 338. P. 991-1037. doi
Van H. D., Lowen W. The Gerstenhaber–Schack complex for prestacks // Advances in Mathematics. 2018. Vol. 330. P. 173-228. doi
Karzhemanov I., Zhdanovskiy I. Some properties of surjective rational maps // European Journal of Mathematics. 2018. Vol. 4. No. 1. P. 326-329. doi
Verbitsky M., Sampaio J. E., Birbrair L., Fernandes A. Multiplicity of singularities is not a bi-Lipschitz invariant / Cornell University. Series arxive "math". 2018. 
Verbitsky M., Solomon J. P. Locality in the Fukaya category of a hyperkähler manifold / Cornell University. Series arxive "math". 2018. 
Румынин Д. А., Hristova K. Kac–Moody groups and cosheaves on Davis building // Journal of Algebra. 2018. Vol. 515. P. 202-235. doi
Verbitsky M., Entov M. Unobstructed symplectic packing by ellipsoids for tori and hyperkahler manifolds // Selecta Mathematica, New Series. 2018. Vol. 24. No. 3. P. 2625-2649. doi
Kaledin D. Witt vectors as a polynomial functor // Selecta Mathematica, New Series. 2018. Vol. 24. No. 1. P. 359-402. doi
Krylov V. Integrable Crystals and Restriction to Levi Subgroups Via Generalized Slices in the Affine Grassmannian // Функциональный анализ и его приложения. 2018. Vol. 52. No. 2. P. 113-133. doi
Michael F., Andrei I. Kostka-Shoji polynomials and Lusztig's convolution diagram // Bulletin of the Institute of Mathematics Academia Sinica (New Series). 2018. Vol. 13. No. 1. P. 31-42. doi
Polishchuk A., Lekili Y. Homological mirror symmetry for higher dimensional pairs of pants / Cornell University. Series arxive "math". 2018. 
Kuznetsov A., Debarre O. Gushel-Mukai varieties: Classification and birationalities // Algebraic Geometry. 2018. Vol. 5. No. 1. P. 15-76. doi
Prokhorov Y., Kuznetsov A., Shramov K. Hilbert schemes of lines and conics and automorphism groups of Fano threefolds // Japanese Journal of Mathematics. 2018. Vol. 13. No. 1. P. 109-185. doi
Прохоров Ю. Г. Проблема рациональности для расслоений на коники // Успехи математических наук. 2018. Т. 73. № 3. C. 3-88. doi
Feigin E., Makedonskyi I., Orr Daniel Generalized Weyl modules and nonsymmetric q-Whittaker functions // Advances in Mathematics. 2018. Vol. 330. P. 997-1033. doi
Cheltsov I., Dubouloz A., Park J. Super-rigid affine Fano varieties // Compositio Mathematica. 2018. Vol. 154. No. 11. P. 2462-2484. doi
Verbitsky M., Vuletescu V., Ornea L. Flat affine subvarieties in Oeljeklaus-Toma manifolds / Cornell University. Series arxive "math". 2018. 
Prokhorov Y., Duncan A., Cheltsov I., Blanc J. Finite quasisimple groups acting on rationally connected threefolds / Cornell University. Series math "arxiv.org". 2018. 
Prokhorov Y., Zaidenberg M. Fano-Mukai fourfolds of genus 10 as compactifications of C4 // European Journal of Mathematics. 2018. Vol. 4. No. 3. P. 1197-1263. doi
Blokh A., Oversteegen L., Timorin V. Dynamical generation of parameter laminations, in: Contemporary Mathematics 744 Dynamics: Topology and Numbers (2020). United States of America : American Mathematical Society, 2020. С. 205-229. 
Kuznetsov A., Debarre O. Double covers of quadratic degeneracy and Lagrangian intersection loci / Cornell University. Series arxive "math". 2018. 
Buonerba F., Bogomolov F. A. Dominant classes of projective varieties // European Journal of Mathematics. 2018. Vol. 4. No. 4. P. 1412-1420. doi
Bogomolov F. A., Fu Hang Elliptic curves with large intersection of projective torsion points // European Journal of Mathematics. 2018. Vol. 4. No. 2. P. 555-560. doi
Polishchuk A., Lekili Y. Derived equivalences of gentle algebras via Fukaya categories / Cornell University. Series arxive "math". 2018. 
Kuznetsov A., Shinder E., Karmazyn J. Derived categories of singular surfaces / Cornell University. Series arxive "math". 2018. 
Kuznetsov A., Perry A. Derived categories of Gushel-Mukai varieties // Compositio Mathematica. 2018. Vol. 154. No. 7. P. 1362-1406. doi
Fonarev A., Kuznetsov A. Derived Categories of Curves as Components of Fano Manifolds // Journal of the London Mathematical Society. 2018. Vol. 97. No. 2. P. 24-46. doi
Cheltsov I., Zhang K. Delta invariants of smooth cubic surfaces / Cornell University. Series arxive "math". 2018. 
Cheltsov I., Shramov K., Park J. Delta invariants of singular del Pezzo surfaces / Cornell University. Series math "arxiv.org". 2018. 
Rumynin D. D-affinity and Rational Varieties / Cornell University. Series arxive "math". 2018. 
Finkelberg M. V., Braverman A. Coulomb branches of 3-dimensional gauge theories and related structures / Cornell University. Series arxive "math". 2018. 
Sechin P. Chern classes from Morava K-theories to p^n-typical oriented theories / Cornell University. Series arxive "math". 2018. 
Kuznetsov A., Perry A. Categorical joins / Cornell University. Series arxive "math". 2018. 
Polishchuk A., Johnson D. Birational models of M_2,2 arising as moduli of curves with nonspecial divisors / Cornell University. Series arxive "math". 2018. 
Sechin P., Semenov N. Applications of the Morava K-theory to algebraic groups / Cornell University. Series arxive "math". 2018. 
Bogomolov F. A., Halle L. H., Pazuki F., Tanimoto S. Abelian Calabi–Yau threefolds: Néron models and rational points // Mathematical Research Letters. 2018. Vol. 25. No. 2. P. 367-392. doi
Finkelberg M. V., Braverman A. A quasi-coherent description of the the category of D-mod(Gr_GL(n)) / Cornell University. Series arxive "math". 2018. 
Wendland A., Rumynin D. 2-Groups, 2-characters, and Burnside rings // Advances in Mathematics. 2018. Vol. 338. P. 196-236. doi
Yanki L., Polishchuk A. Auslander orders over nodal stacky curves and partially wrapped Fukaya categories // Journal of Topology. 2018. Vol. 11. No. 3. P. 615-644. doi
Polishchuk A. A∞-algebras associated with elliptic curves and Eisenstein–Kronecker series // Selecta Mathematica, New Series. 2018. Vol. 24. No. 1. P. 563-589. doi
Bondal A. I., Bodzenta-Skibinska A. Canonical tilting relative generators // Advances in Mathematics. 2018. Vol. 323. P. 226-278. doi
Verbitsky M., Fino A., Grantcharov G. Algebraic dimension of complex nilmanifolds // Journal de Mathématiques Pures et Appliquées. 2018. Vol. 9. No. 118. P. 204-218. doi
Kaledin D. Bokstein homomorphism as a universal object // Advances in Mathematics. 2018. Vol. 324. P. 267-325. doi
Blokh A., Oversteegen L., Ptacek R., Timorin V. Complementary Components to the Cubic Principal Hyperbolic Domain // Proceedings of the American Mathematical Society. 2018. Vol. 146. No. 11. P. 4649-4660. doi
Cheltsov I., Park J., Shramov K. Alpha-invariants and purely log terminal blow-ups // European Journal of Mathematics. 2018. Vol. 4. No. 3. P. 845-858. doi
Polishchuk A. Contracting the Weierstrass locus to a point, in: String-Math 2016. Volume 98 of Proceedings of Symposia in Pure Mathematics.: American Mathematical Society, 2018. С. 241-257. 
Rovinsky M. 0-cycles on Grassmannians as representations of projective groups / Cornell University. Series arxive "math". 2018.