# Personal Homepage of Andreas Krug

Since April 2020, I am working as a lecturer at the Institute of Algebraic Geometry at University of Hannover.

Before, I was an assistant in the Sönke Rollenske's research group in Marburg. Prior to that, I was a visiting fellow at the University of Warwick founded by the DFG (German Research Foundation) where my host was Miles Reid, and a postdoc in Bonn in the group of Daniel Huybrechts.

I wrote my PhD thesis as a student of Marc Nieper-Wißkirchen at the University of Augsburg.

Research interests

Derived categories of coherent sheaves

Hilbert schemes of points on surfaces

Calabi-Yau varieties

### Publications

Endomorphism Algebras of Equivariant Exceptional Collections. With Erik Nikolov. Preprint arXiv:2403.19814, 15 pages.

Hochschild cohomology of Hilbert schemes of points on surfaces. With Pieter Belmans and Lie Fu. Preprint arXiv:2309.06244, 45 pages.

Extension Groups of Tautological Bundles on Punctual Quot Schemes of Curves. Preprint arXiv: 2305.17124, 27 pages

Asymmetry of P-functors. With Andreas Hochenegger. Preprint arXiv:2303.03436, 7 pages. To appear in Kyoto Math. J.

Relations among P-Twists. With Andreas Hochenegger. Preprint arXiv:2207.14120, 16 pages.

Compactified Jacobians of Extended ADE curves and Lagrangian Fibrations. With Adam Czapliński, Manfred Lehn, and Sönke Rollenske. Preprint arXiv:2206.11686. 38 pages. To appear in Commun. Contemp. Math.

Extension groups of Tautological Bundles on Symmetric Products of Curves. Beitr. Algebra Geom. 64 (2023), no. 2, 493-530.

Discriminant of Tautological Bundles on Symmetric Products of Curves. Preprint arXiv:2103.07787, 6 pages.

Derived categories of (nested) Hilbert schemes. With Pieter Belmans. Michigan Math. J. 74 (2024), no. 1, 167--187.

Fourier--Mukai Transformation and Logarithmic Higgs Bundles on punctual Hilbert schemes. With Indranil Biswas. J. Geom. Phys. 150 (2020), 103597, 18 pages.

Stability of Tautological Bundles on Symmetric Products of Curves. Math. Res. Lett. 27 (2020), no. 6, 1785--1800

Some ways to reconstruct a sheaf from its tautological image on a Hilbert scheme of points. With Jørgen Rennemo. Math. Nachr. 295 (2022), no. 1, 158–174.

Universal functors on symmetric quotient stacks of Abelian varieties. With Ciaran Meachan. Selecta Math. (N.S.) 28 (2022), no. 2, Paper No. 28, 37 pp.

Formality of P-objects. With Andreas Hochenegger. Compos. Math. 155 (2019), no. 5, 973–994.

Derived categories of resolutions of cyclic quotient singularities. With David Ploog and Pawel Sosna. Q. J. Math. 69 (2018), no. 2, 509–548.

Remarks on the derived McKay correspondence for Hilbert schemes of points and tautological bundles. Math. Ann. 371 (2018), no. 1–2, 461–486.

Varieties with P-units. Trans. Amer. Math. Soc. 370 (2018), no. 11, 7959–7983.

Symmetric quotient stacks and Heisenberg actions. Math. Z. 288 (2018), no. 1–2, 11–22.

Equivalences of equivariant derived categories. With Pawel Sosna. J. Lond. Math. Soc. (2) (2015), no. 1, 19–40.

P-functor versions of the Nakajima operators. Alg. Geom. 6 (2019), 678--715.

On the derived category of the Hilbert scheme of points on an Enriques surface. With Pawel Sosna. Selecta Math. (N.S.) 21 (2015), no. 4, 1339–1360.

Spherical functors on the Kummer surface. With Ciaran Meachan. Nagoya Math. J. 219 (2015), 1–8.

On derived autoequivalences of Hilbert schemes and generalised Kummer varieties. Int. Math. Res. Not. 20 (2015), 10680-10701.

Tensor products of tautological bundles under the Bridgeland-King-Reid-Haiman equivalence. Geom. Dedicata 172 (2014), 245-291.

Extension groups of tautological sheaves on Hilbert schemes. J. Algebraic Geom. 23 (2014), no.3, 571-598.

Here is an electronic copy of my Habilitation thesis. The body of the thesis consists of nine of the above research papers. However, there is a long introduction (25 pages) which might be of some interest. It gives a summary of the papers of mine and makes an attempt to give an overview of related work of other authors on derived categories.

### Talks

Videos of a mini course (three lectures) on derived categories and the McKay correspondence that I gave at the Winter School on Algebraic Surfaces at KIAS (Seoul) in January 2016. (The above link directs to the KIAS Media Archive. There, the videos can be found in the category 'Center & Programs' not 'Mathematics'.)

Beamer slides of a short talk on Hilbert schemes, symmetric quotient stacks, and categorical Heisenberg actions that I gave at the Workshop on Lie Theory in Rauischholzhausen in March 2016.

Beamer slides of my Habilitation talk (in German language) on the Weil Conjectures that I gave at the University of Marburg in November 2017.