Profile
Key facts
My name is Ben Anthes and I used to be a mathematician in algebraic geometry at the Philipps University Marburg in the group of Sönke Rollenske.Mathematical interests and education
Major
The main focus of my research is motivated by the theory of moduli of varieties of general type. In my thesis, supervised by Sönke Rollenske at the Philipps University Marburg, I analysed a stratification of the moduli space of Gorenstein stable surfaces \(X\) satisfying \(K_X^2 = 2\) and \(\chi(\mathcal{O}_X) = 4\). It can be obtained for free from the university's publication server here.
My only current (recreational) project is a write-up and some macaulay2-computations concerning base-points of adjoint linear systems. That was supposed to become my thesis project, but couldn't be finished in time. The objective was to prove a Reider-type theorem for adjoint linear systems on semi-log canonical surfaces. I'll happily share what I've learnt. It may take some time to finish the write-up since I'm not allocating much of my spare time.
Undergraduate theses
I've written my Bachelor's and Master's theses at the Johannes Gutenberg University Mainz, Germany, under the supervision of Manfred Lehn. The Master's thesis investigates (sheaves) of Clifford algebras associated with degenerate quadratic modules, led by the question when they are Azumaya. The Bachelor's thesis generalises an important formula in local Kähler geometry, due to Weil, thereby relating it with the canonical \(\mathfrak{sl}_2\)-representation. See this pdf for an english summary.Further/Minor interests
- Deformation limits of projective varieties internal to complex analytic or algebraic spaces.
- Connections between algebraic geometry and homological algebra, representation-, or invariant theory; birational invariants through derived categories; Azumaya algebras and Brauer-Severi schemes...
- Holomorphic symplectic varieties; Lagrangian fibrations thereof.
- Categorical homotopy theory, homotopical algebra, derived methods in algebraic geometry.
Publications
- Ben Anthes, Andrea Cattaneo, Sönke Rollenske and Adriano Tomassini: \(\partial\overline{\partial}\)-complex symplectic and Calabi-Yau manifolds: Albanese map, deformations and period maps, Annals of Global Analysis and Geometry Volume 54, Issue 3, October 2018 p. 377-398, Springer 'Online First', DOI 10.1007/s10455-018-9607-3 (arXiv:1711.05107)
- Ben Anthes: Gorenstein stable surfaces satisfying \(K_X^2 = 2\) and \(\chi(\mathcal O_X) = 4\), Dissertation, Philipps-University Marburg, 2018, DOI 10.17192/z2019.0050
- Ben Anthes: Gorenstein stable surfaces with \(K_X^2 = 2\) and \(\chi(\mathcal O_X) = 4\), Annali SNS di Pisa Vol. XXI, issue special (pp. 1137-1186), DOI 10.2422/2036-2145.201812_006 (also see arXiv:1904.12307 and the gitlab repository for Macaulay2 code)
Selected Talks
- Complex symplectic varieties satisfying the \(\partial\overline{\partial}\)-Lemma; Cohomology of Complex Manifolds and Special Structures (Conference), June 2018, Levico Terme, Italy
- Gorenstein stable surfaces with \(K_{X}^2 = 2\) and \(\chi(\mathcal{O}_{X}) = 4\); Junior Algebraic Geometry Seminar in Warwick, April 2018, Coventry, UK
- Base-points of adjoint linear systems on singular algebraic surfaces; GAeL XXV (Conference), June 2017, Bath, UK
- On Atiyah's "The non-existent complex \(6\)-sphere"; (Non)-Existence of complex structures on \(S^6\) (Workshop), March 2017, Marburg, Germany
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