On Cohen-Macaulay modules over non-commutative surface singularities

?

On Cohen-Macaulay modules over non-commutative surface singularities

Central European Journal of Mathematics. 2014. Vol. 12. No. 5. P. 675–687.

Drozd Y., Gavran V.

We generalize the results of Kahn about a correspondence between Cohen-Macaulay modules and vector bundles to non-commutative surface singularities. As an application, we give examples of non-commutative surface singularities which are not Cohen-Macaulay finite, but are Cohen-Macaulay tame.

Language: English

DOI

Text on another site

Explicit constructions of bordism of Milnor hypersurface H1,n and CP1 × CPn−1

Solomadin G., Journal of the Mathematical Society of Japan 2020 Vol. 3 P. 765–776

In the present paper we construct two new explicit complex bordisms between any two projective bundles over $\mathbb{C} P^1$ of the same complex dimension, including the Milnor hypersurface $H_{1,n}$ and $\mathbb{C} P^1\times \mathbb{C} P^{n-1}$. These constructions reduce the bordism problem to the null-bordism of some projective bundle over $\mathbb{C} P^1$ with the non-standard stably complex ...

Added: September 20, 2021

Stable vector bundles on the families of curves

Bogomolov F. A., Lukzen E., / Series arXiv "math". 2020.

We offer a new approach to proving the Chen-Donaldson-Sun theorem which we demonstrate with a series of examples. We discuss the existence of a construction of a special metric on stable vector bundles over the surfaces formed by a families of curves and its relation to the one-dimensional cycles in the moduli space of stable ...

Added: October 27, 2020

Modified Elliptic Genus

Gritsenko V., , in: Partition Functions and Automorphic Forms.: Springer Publishing Company, 2020. P. 87–119.

Abstract This mini course is an additional part to my semester course on the theory of Jacobi modular forms given at the mathematical department of NRU HSE in Moscow (see Gritsenko Jacobi modular forms: 30 ans après; COURSERA (12 lectures and seminars), 2017–2019). This additional part contains some applications of Jacobi modular forms to the ...

Added: October 26, 2020

Symplectic instanton bundles on ℙ3 and ’t Hooft instantons

Bruzzo U., Markushevich D., Tikhomirov A. S., European Journal of Mathematics 2016 Vol. 2 P. 73–86

We study the moduli space $I_{n,r}$In,r of rank-2r symplectic instanton vector bundles on $\mathbb{P}^3$ℙ3 with $r\ge 2$r⩾2 and second Chern class $n\ge r+1, n-r\equiv 1(\mathrm{mod} 2)$n⩾r+1,n−r≡1(mod2). We introduce the notion of tame symplectic instantons by excluding a kind of pathological monads and show that the locus $I_{n,r}^*$I∗n,r of tame symplectic instantons is irreducible and has the expected dimension equal to ...

Added: December 28, 2015

Moduli of symplectic instanton vector bundles of higher rank on projective space $\mathbb{P}^3$

Tikhomirov A. S., Bruzzo U., Markushevich D., Central European Journal of Mathematics 2012 Vol. 10 No. 4 P. 1232–1245

Symplectic instanton vector bundles on the projective space $\mathbb{P}^3$ constitute a natural generalization of mathematical instantons of rank-2. We study the moduli space $I_{n;r}$ of rank-$2r$ symplectic instanton vector bundles on $\mathbb{P}^3$ with $r\ge2$ and second Chern class $n\ge r, n\equiv r(\mod 2)$. We introduce the notion of tame symplectic instantons by excluding a kind ...

Added: October 21, 2014

Bubble tree compactification of moduli spaces of vector bundles on surfaces

Tikhomirov A. S., Markushevich D., Trautmann G., Central European Journal of Mathematics 2012 Vol. 19 No. 4 P. 1331–1355

We announce some results on compactifying moduli spaces of rank 2 vector bundles on surfaces by spaces of vector vector bundles on trees of surfaces. This is thought as an algebraic counterpart of the so-called bubbling of vector bundled connections an in differential geometry. The new moduli spaces are algebraic spaces arising as quotients ...

Added: October 21, 2014