Research

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.

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

Here is a list of my papers and preprints.

  • 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? To appear in BUMI volume dedicated to Workshop on algebraic surfaces.arXiv:1605.04803. (Survey.)

  • C. Fontanari, S. Diverio, D. Martinelli, Rational curves on fibered Calabi-Yau manifolds. To appear in Documenta Mathematica. arXiv:1607.01561.

  • D. Martinelli, S. Schreieder, L. Tasin, On the number and boundedness of log minimal models of general type. To appear in the Annales scientifiques de l'ENS. arXiv:1610.08932.

  • C. Fontanari, D. Martinelli, A remark on rationally connected varieties and Mori Dream Spaces. To appear on the Proceedings of the Edinburgh Mathematical Society. arXiv:1706.05200.

  • D. Martinelli, Effective bounds for the number of minimal model programs of a smooth threefold. Submitted. arXiv:1612.0544.

Upcoming works.

  • 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.

Countries where I gave a maths talk.

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Diletta
Martinelli

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