How Long to Read Towards a Bezout-type Theory of Affine Varieties

How Long Does it Take to Read Towards a Bezout-type Theory of Affine Varieties?

It takes the average reader 3 hours and 43 minutes to read Towards a Bezout-type Theory of Affine Varieties by Pinaki Mondal

Assuming a reading speed of 250 words per minute. Learn more

Description

We study projective completions of affine algebraic varieties (defined over an algebraically closed field K ) which are given by filtrations, or equivalently, integer valued 'degree like functions' on their rings of regular functions. For a polynomial map P := (P1, ..., Pn) : X → Kn of affine varieties with generically finite fibers, we prove that there are completions of the source such that the intersection of completions of the hypersurfaces {Pj = aj} for generic (a1, ..., a n) ∈ Kn coincides with the respective fiber (in short, the completions 'do not add points at infinity' for P). Moreover, we show that there are 'finite type' completions with the latter property, i.e. determined by the maximum of a finite number of 'semidegrees', by which we mean degree like functions that send products into sums. We characterize the latter type completions as the ones for which ideal I of the 'hypersurface at infinity' is radical. Moreover, we establish a one-to-one correspondence between the collection of minimal associated primes of I and the unique minimal collection of semidegrees needed to define the corresponding degree like function. We also prove an 'affine Bezout type' theorem for polynomial maps P with finite fibers that admit semidegrees corresponding to completions that do not add points at infinity for P. For a wide class of semidegrees of a 'constructive nature' our Bezout-type bound is explicit and sharp.

How long is Towards a Bezout-type Theory of Affine Varieties?

Towards a Bezout-type Theory of Affine Varieties by Pinaki Mondal is 222 pages long, and a total of 55,944 words.

This makes it 75% the length of the average book. It also has 68% more words than the average book.

How Long Does it Take to Read Towards a Bezout-type Theory of Affine Varieties Aloud?

The average oral reading speed is 183 words per minute. This means it takes 5 hours and 5 minutes to read Towards a Bezout-type Theory of Affine Varieties aloud.

What Reading Level is Towards a Bezout-type Theory of Affine Varieties?

Towards a Bezout-type Theory of Affine Varieties is suitable for students ages 12 and up.

Note that there may be other factors that effect this rating besides length that are not factored in on this page. This may include things like complex language or sensitive topics not suitable for students of certain ages.

When deciding what to show young students always use your best judgement and consult a professional.

Where Can I Buy Towards a Bezout-type Theory of Affine Varieties?

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