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Alessandro Bigazzi


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On the 15th of June 2020 I successfully defended my PhD. If you want to contact me, please use the non-Warwick email account.

I worked in the Algebraic Geometry group under the supervision of Christian Böhning. My thesis title is Stable rationality and degenerations of conic bundles; contact me if you are interested in further information.

I've earned a Bachelor of Sciences in mathematics at Università di Firenze (Italy), advisod by Professor Fabio Vlacci, and a Master of Science in pure mathematics at Università Roma Tre (Italy), with the final dissertation Castelnuovo-Mumford regularity for projective curves, advised by Professor Edoardo Sernesi.

Research interests.

  • Rationality problems for 3-folds and 4-folds quadric fibrations:
    • Geometry of high-dimensional varieties.
    • Geometric and log-geometric obstructions to decomposition ot the diagonal.
    • Algebraic invariants in wild characteristic settings
  • Quadric fibrations:
    • rationality and stable rationality of 3-fold conic bundles
    • local geometry for conic bundles in characteristic 2
  • Brauer group and unramified Brauer group:
    • the p-primary torsion part of the Brauer group
    • Brauer group of conic bundles and invariance properties
    • reciprocity-like properties for quadric fibrations in characteristic 2
  • Crystalline and rigid cohomology approach to the above problems.

Contact information.

E-mail: alessandro.bigazzi <at> hotmail.com

Publications.

  1. (with A.Auel, Ch. Boehning, H.Ch. Graf von Bothmer) Universal triviality of the Chow group of 0-cycles and the Brauer group, to appear in IMRN
  2. (with A.Auel, Ch. Boehning, H.Ch Graf von Bothmer) Unramified Brauer group of conic bundle threefolds in characteristic two, to appear in AJM

Teaching.

A.Y. 2019-20: TA for Complex Analysis (3rd year)
A.Y. 2019-20
: TA for Geometry (2nd year)
A.Y. 2019-20
: TA for Introduction to Topology (3rd year)
A.Y. 2019-20
: Supervisor of 2nd year Mathematics students.

A.Y. 2018-19: TA for Complex Analysis (3rd year)
A.Y. 2018-19:
TA for Geometry (2nd year).
A.Y. 2018-19:
TA for Introduction to Topology (3rd year).
A.Y. 2018-19: Supervision of 2nd year Mathematics students.

A.Y. 2017-18: TA for Metric Spaces (2nd year, with exam marking)
A.Y. 2017-18:
TA for Commutative Algebra (3rd year)
A.Y. 2017-18:
TA for Introduction to Topology (3rd year)
A.Y. 2017-18:
Supervision of 2nd year Mathematics students.

A.Y. 2016-17: Supervision of 1st and 2nd year Mathematics students.

A.Y. 2015-16: Exercise sessions for Algebraic Geometry 2 - Schemes and Cohomology (Univ. Roma 3)

A.Y. 2012-13: Exercise sessions for Geometry III - Algebraic topology (Univ. di Firenze)
A.Y. 2012-13: Exercise sessions for Differential Topology (Univ. di Firenze)

Further material.

Some notes on Van Kampen's theorem, written during an undergraduate course in algebraic topology.

An Essay on the stable Lüroth problem, written in my first year of doctoral study.