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Ilya Smirnov

Ikerbasque Research Fellow

Singularity Theory and Algebraic Geometry

T +34 946 567 842
F +34 946 567 842
E ismirnov@bcamath.org

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Ikerbasque profile

I am a Ramón y Cajal and Ikerbasque Research Fellow at BCAM since 2022. Personal webpage. 

My principal research area is local algebra; loosely speaking this means that I study singularities, as local rings, using techniques of commutative algebra. A particular way to do so is via numerical invariants, numbers that are supposed to represent an aspect of the complexity. 

 

  • Stability and deformation of F-singularities 

    De Stefani, A.; Smirnov, I.Autoridad BCAM (2024-12-01)
    We study the problem of m-adic stability of F-singularities, that is, whether the property that a quotient of a local ring (R,m) by a non-zero divisor x∈m has good F-singularities is preserved in a sufficiently small m-adic ...

  • Effective generic freeness and applications to local cohomology 

    Cid-Ruiz, Y.; Smirnov, I.Autoridad BCAM (2024-10-01)
    Let (Formula presented.) be a Noetherian domain and (Formula presented.) be a finitely generated (Formula presented.) -algebra. We study several features regarding the generic freeness over (Formula presented.) of an ...

  • Lower bounds on Hilbert-Kunz multiplicities and maximal F-signature 

    Jeffries, J.; Nakajima, Y.; Smirnov, I.Autoridad BCAM; Watanabe, K.; Yoshida, K. (2022)
    ABSTRACT. Hilbert–Kunz multiplicity and F-signature are numerical invariants of commutative rings in positive characteristic that measure severity of singularities: for a regular ring both invariants are equal to one and ...

  • Uniform Lech's inequality 

    Ma, L.; Smirnov, I.Autoridad BCAM (2022)
    Let (R,m) be a Noetherian local ring, and let M be a finitely generated R-module of dimension d. We prove that the set [Formula presented] is bounded below by 1/d!e(R‾) where R‾=R/Ann(M). Moreover, when Mˆ is equidimensional, ...

  • Uniform Lech's inequality 

    Ma, L.; Smirnov, I.Autoridad BCAM (2022)
    Let (R,m) be a Noetherian local ring of dimension d ≥ 2. We prove that if e(R􏰊red) > 1, then the classical Lech’s inequality can be improved uniformly for all m-primary ideals, that is, there exists ε > 0 such that e(I) ...

More information

 

School on Commutative Algebra and Algebraic Geometry in Prime Characteristics, ICTP Trieste, May 2-5, 2023.

BCAM Severo Ochoa course "Introduction to multiplicity theory" Spring 2023. 

RGAS School on Singularities, IMUS Sevilla, January 8-12, 2024.