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Vanishing Theorems and their Applications in Syzygies, Deformation Theory and Hodge Theory
Basu, Debjit
Basu, Debjit
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Abstract
We investigate new vanishing theorems in Syzygies, Deformation theory and Hodge theory. As applications, in the second chapter, we prove results on syzygies of projective varieties from the end of the resolution. In the third chapter, we study nowhere reduced double structures on elliptic ruled surfaces that arise in deformation theory of abelian surfaces. In the fourth chapter, we study Bott vanishing, Torelli theorems for hypersurfaces and Nori connectivity on ruled varieties. The first chapter is dedicated to establish connection between these seemingly different areas.
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2026-05-31
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University of Kansas
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Basu_ku_0099D_20453.pdf
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Algebraic geometry, Deformation, Hodge theory, Syzygies