Research

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My research interests are in algebraic geometry and in particular in higher dimensional birational geometry. My work aims to study effectivity questions on algebraic varieties related to their underlying topology as complex manifolds. I am also interested in positive characteristic methods, moduli spaces and Calabi-Yau manifolds. I am currently interested in the interplay between birational geometry of moduli spaces of K3s surfaces and Bridgeland stability conditions.

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Check out my PhD student: Przemysław Grabowski.

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If you would like to have an introduction about my research area have a look at this poster (made jointly with Andrea Fanelli).

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Here is a list of my papers and preprints in Algebraic Geometry.

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• D. Martinelli, Y. Nakamura, J. Witaszek, On the base point free theorem for log canonical threefold over the algebraic closure of a finite field. Algebra & Number Theory, Vol. 9, (2015) 725-747. arXiv:1407.5146.

• D. Martinelli, J.C. Naranjo, G.P. Pirola, Connectedness Bertini Theorem via Numerical equivalence. Advances in Geometry, Vol.17, (2017), no.1, 31-38. arXiv:1412.1978.

• C. Fontanari, D. Martinelli, Why should a birational geometer care about Bridgeland stability conditions? Boll. Unione Mat. Ital. (2018) 11:69–74. arXiv:1605.04803. 

• C. Fontanari, S. Diverio, D. Martinelli, Rational curves on fibered Calabi-Yau manifolds. Documenta Mathematica 24 (2019) 663–675. arXiv:1607.01561.

• D. Martinelli, S. Schreieder, L. Tasin, On the number and boundedness of log minimal models of general type. Ann. Scient. Éc. Norm. Sup. 4e série, 53, (2020), 1181--1205. arXiv:1610.08932.

• C. Fontanari, D. Martinelli, A remark on rationally connected varieties and Mori Dream Spaces. Proceedings of the Edinburgh Mathematical Society 62 (2019) 259-263. arXiv:1706.05200.

• D. Martinelli, Effective bounds for the number of minimal model programs of a smooth threefold. Glasgow Math. J. 64 (2022) 106-113. arXiv:1612.0544.

• A. Bayer, S. Beentjes, S, Feyzbakhsh, G. Hein, D. Martinelli, F. Rezaee, B. Schmidt, The desingularization of the theta divisor of a cubic threefold as a moduli space, Accepted for publication in Geometry&Topology. arXiv:2011.12240.

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Upcoming works.

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• D. Martinelli, On the geometry of contractions of the moduli space of sheaves on a K3 surface. In preparation.

• C. Araujo, A.M. Castravet, I. Kaur, D. Martinelli, Gale duality, Blowups and moduli spaces. In preparation.

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I gave over 50 invited talks in research seminars and International conferences in over five continents. See here for a full list.

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